Systems and methods of object shape and position determination in three-dimensional (3D) space

ABSTRACT

Methods and systems for capturing motion and/or determining the shapes and positions of one or more objects in 3D space utilize cross-sections thereof. In various embodiments, images of the cross-sections are captured using a camera based on edge points thereof.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.15/387,353 filed 21 Dec. 2016, entitled “SYSTEMS AND METHODS OF OBJECTSHAPE AND POSITION DETERMINATION IN THREE-DIMENSIONAL (3D) SPACE”, (nowU.S. Pat. No. 9,741,136, issued 22 Aug. 2017), which is a continuationof U.S. patent application Ser. No. 14/710,499, filed May 12, 2015,entitled “SYSTEMS AND METHODS OF OBJECT SHAPE AND POSITION DETERMINATIONIN THREE-DIMENSIONAL (3D) SPACE”, (now U.S. Pat. No. 9,697,643, issued 4Jul. 2017), which is a continuation of U.S. patent application Ser. No.14/106,140 filed Dec. 13, 2013, (now U.S. Pat. No. 9,153,028, issuedOct. 6, 2015), entitled “SYSTEMS AND METHODS FOR CAPTURING MOTION INTHREE-DIMENSIONAL SPACE”, which is a continuation of U.S. patentapplication Ser. No. 13/742,953 filed Jan. 16, 2013 (now U.S. Pat. No.8,638,989 issued Jan. 28, 2014), entitled “SYSTEMS AND METHODS FORCAPTURING MOTION IN THREE-DIMENSIONAL SPACE”, which is acontinuation-in-part of U.S. patent application Ser. No. 13/414,485filed Mar. 7, 2012, entitled “MOTION CAPTURE USING CROSS-SECTIONS OF ANOBJECT”, and Ser. No. 13/724,357 filed Dec. 21, 2012, (now U.S. Pat. No.9,070,019, issued Jun. 30, 2015), entitled “SYSTEMS AND METHODS FORCAPTURING MOTION IN THREE-DIMENSIONAL SPACE”. U.S. patent applicationSer. No. 13/724,357 claims priority to and the benefit of U.S.Provisional Patent Application No. 61/724,091 filed Nov. 8, 2012,entitled “SYSTEMS AND METHODS FOR CAPTURING MOTION IN THREE-DIMENSIONALSPACE”, and U.S. patent application Ser. No. 13/414,485 claims priorityto and the benefit of U.S. Provisional Patent Application No. 61/587,554filed Jan. 17, 2012, entitled “METHODS AND SYSTEMS FOR IDENTIFYINGPOSITION AND SHAPE OF OBJECTS IN THREE-DIMENSIONAL SPACE”. Said U.S.patent application Ser. No. 13/724,357 is also a continuation-in-part ofU.S. patent application Ser. No. 13/414,485.

This application is related to U.S. patent application Ser. No.14/710,512, filed May 12, 2015 entitled “SYSTEMS AND METHODS OFCONSTRUCTING THREE-DIMENSIONAL (3D) MODEL OF AN OBJECT USING IMAGECROSS-SECTIONS” filed May 12, 2016 (now U.S. Pat. No. 9,436,998). Therelated application is incorporated by reference in this application.

FIELD OF THE INVENTION

The present invention relates, in general, to image analysis, and inparticular embodiments to identifying shapes and capturing motions ofobjects in three-dimensional space.

BACKGROUND

Motion capture has numerous applications. For example, in filmmaking,digital models generated using motion capture can be used as the basisfor the motion of computer-generated characters or objects. In sports,motion capture can be used by coaches to study an athlete's movementsand guide the athlete toward improved body mechanics. In video games orvirtual reality applications, motion capture can be used to allow aperson to interact with a virtual environment in a natural way, e.g., bywaving to a character, pointing at an object, or performing an actionsuch as swinging a golf club or baseball bat.

The term “motion capture” refers generally to processes that capturemovement of a subject in three-dimensional (3D) space and translate thatmovement into, for example, a digital model or other representation.Motion capture is typically used with complex subjects that havemultiple separately articulating members whose spatial relationshipschange as the subject moves. For instance, if the subject is a walkingperson, not only does the whole body move across space, but the positionof arms and legs relative to the person's core or trunk are constantlyshifting. Motion capture systems are typically interested in modelingthis articulation.

Most existing motion capture systems rely on markers or sensors worn bythe subject while executing the motion and/or on the strategic placementof numerous cameras in the environment to capture images of the movingsubject from different angles. Such systems tend to be expensive toconstruct. In addition, markers or sensors worn by the subject can becumbersome and interfere with the subject's natural movement. Further,systems involving large numbers of cameras tend not to operate in realtime, due to the volume of data that needs to be analyzed andcorrelated. Such considerations of cost, complexity and convenience havelimited the deployment and use of motion capture technology.

Consequently, there is a need for an economical approach that capturesthe motion of objects in real time without attaching sensors or markersthereto.

SUMMARY

Embodiments of the present invention relate to methods and systems forcapturing motion and/or determining the shapes and positions of one ormore objects in 3D space using at least one cross-section thereof; thecross-section(s) may be obtained from, for example, reflections from theobject or shadows cast by the object. In various embodiments, the 3Dreflections or shadows captured using a camera are first sliced intomultiple two-dimensional (2D) cross-sectional images. Thecross-sectional positions and sizes of the 3D objects in each 2D slicemay be determined based on the positions of one or more light sourcesused to illuminate the objects and the captured reflections or shadows.The 3D structure of the object may then be reconstructed by assembling aplurality of the cross-section regions obtained in the 2D slices. Theobjective, in general, is to obtain either a unique ellipse describingthe cross-section of the object, or a subset of the parameters definingthe cross-section (in which case the remaining parameters may beestimated). If there are more light sources than are necessary todetermine the shape of the cross-section, some optimized subset of themmay be utilized for maximum accuracy. The light sources may emit atdifferent wavelengths so that their individual contributions are moreeasily identified, or they may be turned on in sequence rather thansimultaneously, or they may have different brightnesses.

In some embodiments, the 2D cross-section regions are identified basedon a vantage point defined by the position of an image-capturing cameraand shadow edge points generated by light sources. At the vantage point,two light rays are detected; these light rays are transmitted from aleft-edge tangent point and a right-edge tangent point of thecross-section, and define a viewed portion of the cross-section withinthe field of view of the camera. Two equations based on the positions ofthe two edge tangent points can partially determine the characteristicparameters of a closed curve (e.g., an ellipse) approximating thecontour of the object's cross-section. Additionally, each shadow edgepoint created by emitting light from a light source onto thecross-section can provide two equations, one based on the detectedposition of the shadow edge point and the other based on the light rayemitted from the light source to the shadow edge point on thecross-section. Utilizing a suitable number (e.g., one or a plurality) oflight sources can provide sufficient information to determine thecharacteristic parameters of the fitting ellipse, thereby identifyingthe position and size of the cross-section. Accordingly, a 3D model ofthe object can be reconstructed by correlating the determined positionsand sizes of the cross-sections in the 2D slices. A succession of imagescan then be analyzed using the same technique to model motion of theobject.

Accordingly, in a first aspect, the invention pertains to a method ofidentifying a position and shape of an object in 3D space. In variousembodiments, the method comprises using a single camera to capture animage generated by casting an output from at least one source onto theobject; analyzing the image to computationally slice the object into aplurality of 2D slices, each of which corresponds to a cross-section ofthe object, based at least in part on multiple edge points in the image(where an edge point may be, e.g., an illuminated edge point—i.e., apoint on the edge of the object that is detectable by the camera—or ashadow edge point at the boundary of a shadow region, as more fullydescribed below); and reconstructing the position and shape of at leasta portion of the object in 3D space based at least in part on aplurality of the identified cross-sectional positions and sizes. Thesource(s) may be one or more light sources—e.g., one, two, three, ormore than three light-emitting diodes (LEDs). A plurality of lightsources may be operated in a pulsed fashion, whereby a plurality of theedge points are generated sequentially.

In some embodiments, the edge points define a viewed portion of thecross-section within which the portion of the cross-section is within afield of view of an image-capturing device (e.g., a camera). Light rayscast from the edge points to the image-capturing device may be tangentto the cross-section, and at least one shadow edge point may be createdby emitting light from the source(s) onto the object. The shadow edgepoint(s) may be defined by a boundary between a shadow region and anilluminated region on the cross-section of the object.

The method may further comprise defining a 3D model of the object andreconstructing the position and shape of the object in 3D space based onthe 3D model. The position and shape of the object in 3D space may bereconstructed based on correlations between the plurality of the 2Dslices.

In another aspect, the invention pertains to a system for identifying aposition and shape of an object in 3D space. In various embodiments, thesystem comprises a camera oriented toward a field of view; at least onesource to direct illumination onto the object in the field of view; andan image analyzer coupled to the camera and the source(s). The imageanalyzer is configured to capture an image generated by casting anoutput from at least one source onto the object analyze the image tocomputationally slice the object into a plurality of two-dimensional 2Dslices, each of which corresponds to a cross-section of the object,based at least in part on edge points in the image; and reconstruct theposition and shape of at least a portion of the object in 3D space basedat least in part on a plurality of the identified cross-sectionalpositions and sizes. The source(s) may be a plurality of light sources,e.g., one, two, three or more LEDs. The system may include a driver foroperating the sources in a pulsed fashion, whereby a plurality of theshadow edge points are generated sequentially. In some embodiments, theimage analyzer is further configured to define a 3D model of the objectand reconstruct the position and shape of the object in 3D space basedon the 3D model.

Reference throughout this specification to “one example,” “an example,”“one embodiment,” or “an embodiment” means that a particular feature,structure, or characteristic described in connection with the example isincluded in at least one example of the present technology. Thus, theoccurrences of the phrases “in one example,” “in an example,” “oneembodiment,” or “an embodiment” in various places throughout thisspecification are not necessarily all referring to the same example.Furthermore, the particular features, structures, routines, steps, orcharacteristics may be combined in any suitable manner in one or moreexamples of the technology. The headings provided herein are forconvenience only and are not intended to limit or interpret the scope ormeaning of the claimed technology.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, like reference characters generally refer to the sameparts throughout the different views. Also, the drawings are notnecessarily to scale, with an emphasis instead generally being placedupon illustrating the principles of the invention. In the followingdescription, various embodiments of the present invention are describedwith reference to the following drawings, in which:

FIG. 1 is a simplified illustration of a motion capture system accordingto an embodiment of the present invention;

FIG. 2 is a simplified block diagram of a computer system that can beused according to an embodiment of the present invention;

FIGS. 3A (top view) and 3B (side view) are conceptual illustrations ofhow slices are defined in a field of view according to an embodiment ofthe present invention;

FIGS. 4A-4C are top views illustrating an analysis that can be performedon a given slice according to an embodiment of the present invention.FIG. 4A is a top view of a slice. FIG. 4B illustrates projecting edgepoints from an image plane to a vantage point to define tangent lines.FIG. 4C illustrates fitting an ellipse to tangent lines as defined inFIG. 4B;

FIG. 5 graphically illustrates an ellipse in the xy plane characterizedby five parameters;

FIGS. 6A and 6B provide a flow diagram of a motion-capture processaccording to an embodiment of the present invention;

FIG. 7 graphically illustrates a family of ellipses that can beconstructed from four tangent lines;

FIG. 8 sets forth a general equation for an ellipse in the xy plane;

FIG. 9 graphically illustrates how a centerline can be found for anintersection region with four tangent lines according to an embodimentof the present invention;

FIGS. 10A-10N set forth equations that can be solved to fit an ellipseto four tangent 15 lines according to an embodiment of the presentinvention;

FIGS. 11A-11C are top views illustrating instances of slices containingmultiple disjoint cross-sections according to various embodiments of thepresent invention;

FIG. 12 graphically illustrates a model of a hand that can be generatedusing a motion capture system according to an embodiment of the presentinvention;

FIG. 13 is a simplified system diagram for a motion-capture system withthree cameras according to an embodiment of the present invention;

FIG. 14 illustrates a cross-section of an object as seen from threevantage points in the system of FIG. 13;

FIG. 15 graphically illustrates a technique that can be used to find anellipse from at least five tangents according to an embodiment of thepresent invention;

FIGS. 16A, 16B, and 16C are simplified illustrations of a motion-capturesystem in accordance with an embodiment of the present invention;

FIG. 17 schematically illustrates a system for capturing shadows of anobject according to an embodiment of the present invention;

FIG. 18 schematically illustrates an ambiguity that can occur in thesystem of FIG. 17;

FIG. 19 schematically illustrates another system for capturing shadowsof an object according to another embodiment of the present invention;

FIG. 20 graphically depicts a collection of the intersection regionsdefined by a virtual rubber band stretched around multiple intersectionregions in accordance with an embodiment of the invention;

FIG. 21 schematically illustrates a simple intersection regionconstructed using two light sources in accordance with an embodiment ofthe invention;

FIGS. 22A, 22B and 22C schematically depict determinations of trueintersection points in accordance with various embodiments of theinvention;

FIG. 23 schematically depicts an intersection region uniquely identifiedusing a group of the intersection points;

FIG. 24 illustrates an image coordinate system incorporated to definethe locations of the shadows in accordance with an embodiment of theinvention;

FIG. 25A illustrates separate color images captured using color filtersin accordance with an embodiment of the invention;

FIG. 25B depicts a reconstructed 3D image of the object;

FIGS. 26A, 26B, and 26C schematically illustrate a system for capturingan image of both the object and one or more shadows cast by the objectfrom one or more light sources at known positions according to anembodiment of the present invention;

FIG. 27 schematically illustrates a camera-and-beamsplitter setup for amotion capture system according to another embodiment of the presentinvention;

FIG. 28 schematically illustrates a camera-and-pinhole setup for amotion capture system according to another embodiment of the presentinvention; and

FIGS. 29A, 29B, and 29C depict a motion capture system operativelyconnected to a head-mounted device, a mobile device, and anauthentication server, respectively.

DETAILED DESCRIPTION

Embodiments of the present invention relate to methods and systems forcapturing motion and/or determining position of an object using smallamounts of information. For example, an outline of an object's shape, orsilhouette, as seen from a particular vantage point can be used todefine tangent lines to the object from that vantage point in variousplanes, referred to herein as “slices.” Using as few as two differentvantage points, four (or more) tangent lines from the vantage points tothe object can be obtained in a given slice. From these four (or more)tangent lines, it is possible to determine the position of the object inthe slice and to approximate its cross-section in the slice, e.g., usingone or more ellipses or other simple closed curves. As another example,locations of points on an object's surface in a particular slice can bedetermined directly (e.g., using a time-of-flight camera), and theposition and shape of a cross-section of the object in the slice can beapproximated by fitting an ellipse or other simple closed curve to thepoints. Positions and cross-sections determined for different slices canbe correlated to construct a 3D model of the object, including itsposition and shape. A succession of images can be analyzed using thesame technique to model motion of the object. Motion of a complex objectthat has multiple separately articulating members (e.g., a human hand)can be modeled using techniques described herein.

In some embodiments, the silhouettes of an object are extracted from oneor more images of the object that reveal information about the object asseen from different vantage points. While silhouettes can be obtainedusing a number of different techniques, in some embodiments, thesilhouettes are obtained by using cameras to capture images of theobject and analyzing the images to detect object edges.

FIG. 1 is a simplified illustration of a motion capture system 100according to an embodiment of the present invention. System 100 includestwo cameras 102, 104 arranged such that their fields of view (indicatedby broken lines) overlap in region 110. Cameras 102 and 104 are coupledto provide image data to a computer 106. Computer 106 analyzes the imagedata to determine the 3D position and motion of an object, e.g., a hand108, that moves in the field of view of cameras 102, 104.

Cameras 102, 104 can be any type of camera, including visible-lightcameras, infrared (IR) cameras, ultraviolet cameras or any other devices(or combination of devices) that are capable of capturing an image of anobject and representing that image in the form of digital data. Cameras102, 104 are preferably capable of capturing video images (i.e.,successive image frames at a constant rate of at least 15 frames persecond), although no particular frame rate is required. The particularcapabilities of cameras 102, 104 are not critical to the invention, andthe cameras can vary as to frame rate, image resolution (e.g., pixelsper image), color or intensity resolution (e.g., number of bits ofintensity data per pixel), focal length of lenses, depth of field, etc.In general, for a particular application, any cameras capable offocusing on objects within a spatial volume of interest can be used. Forinstance, to capture motion of the hand of an otherwise stationaryperson, the volume of interest might be a meter on a side. To capturemotion of a running person, the volume of interest might be tens ofmeters in order to observe several strides (or the person might run on atreadmill, in which case the volume of interest can be considerablysmaller).

The cameras can be oriented in any convenient manner. In the embodimentshown, respective optical axes 112, 114 of cameras 102 and 104 areparallel, but this is not required. As described below, each camera isused to define a “vantage point” from which the object is seen, and itis required only that a location and view direction associated with eachvantage point be known, so that the locus of points in space thatproject onto a particular position in the camera's image plane can bedetermined. In some embodiments, motion capture is reliable only forobjects in area 110 (where the fields of view of cameras 102, 104overlap), and cameras 102, 104 may be arranged to provide overlappingfields of view throughout the area where motion of interest is expectedto occur.

In FIG. 1 and other examples described herein, object 108 is depicted asa hand. The hand is used only for purposes of illustration, and it is tobe understood that any other object can be the subject of motion captureanalysis as described herein. Computer 106 can be any device that iscapable of processing image data using techniques described herein. FIG.2 is a simplified block diagram of computer system 200 implementingcomputer 106 according to an embodiment of the present invention.Computer system 200 includes a processor 202, a memory 204, a camerainterface 206, a display 208, speakers 209, a keyboard 210, and a mouse211.

Processor 202 can be of generally conventional design and can include,e.g., one or more programmable microprocessors capable of executingsequences of instructions. Memory 204 can include volatile (e.g., DRAM)and nonvolatile (e.g., flash memory) storage in any combination. Otherstorage media (e.g., magnetic disk, optical disk) can also be provided.Memory 204 can be used to store instructions to be executed by processor202 as well as input and/or output data associated with execution of theinstructions.

Camera interface 206 can include hardware and/or software that enablescommunication between computer system 200 and cameras such as cameras102, 104 of FIG. 1. Thus, for example, camera interface 206 can includeone or more data ports 216, 218 to which cameras can be connected, aswell as hardware and/or software signal processors to modify datasignals received from the cameras (e.g., to reduce noise or reformatdata) prior to providing the signals as inputs to a conventionalmotion-capture (“mocap”) program 214 executing on processor 202. In someembodiments, camera interface 206 can also transmit signals to thecameras, e.g., to activate or deactivate the cameras, to control camerasettings (frame rate, image quality, sensitivity, etc.), or the like.Such signals can be transmitted, e.g., in response to control signalsfrom processor 202, which may in turn be generated in response to userinput or other detected events.

In some embodiments, memory 204 can store mocap program 214, whichincludes instructions for performing motion capture analysis on imagessupplied from cameras connected to camera interface 206. In oneembodiment, mocap program 214 includes various modules, such as an imageanalysis module 222, a slice analysis module 224, and a global analysismodule 226. Image analysis module 222 can analyze images, e.g., imagescaptured via camera interface 206, to detect edges or other features ofan object. Slice analysis module 224 can analyze image data from a sliceof an image as described below, to generate an approximate cross-sectionof the object in a particular plane. Global analysis module 226 cancorrelate cross-sections across different slices and refine theanalysis. Examples of operations that can be implemented in code modulesof mocap program 214 are described below.

Memory 204 can also include other information used by mocap program 214;for example, memory 204 can store image data 228 and an object library230 that can include canonical models of various objects of interest. Asdescribed below, an object being modeled can be identified by matchingits shape to a model in object library 230.

Display 208, speakers 209, keyboard 210, and mouse 211 can be used tofacilitate user interaction with computer system 200. These componentscan be of generally conventional design or modified as desired toprovide any type of user interaction. In some embodiments, results ofmotion capture using camera interface 206 and mocap program 214 can beinterpreted as user input. For example, a user can perform hand gesturesthat are analyzed using mocap program 214, and the results of thisanalysis can be interpreted as an instruction to some other programexecuting on processor 200 (e.g., a web browser, word processor or thelike). Thus, by way of illustration, a user might be able to use upwardor downward swiping gestures to “scroll” a webpage currently displayedon display 208, to use rotating gestures to increase or decrease thevolume of audio output from speakers 209, and so on.

It will be appreciated that computer system 200 is illustrative and thatvariations and modifications are possible. Computers can be implementedin a variety of form factors, including server systems, desktop systems,laptop systems, tablets, smart phones or personal digital assistants,and so on. A particular implementation may include other functionalitynot described herein, e.g., wired and/or wireless network interfaces,media playing and/or recording capability, etc. In some embodiments, oneor more cameras may be built into the computer rather than beingsupplied as separate components.

While computer system 200 is described herein with reference toparticular blocks, it is to be understood that the blocks are definedfor convenience of description and are not intended to imply aparticular physical arrangement of component parts. Further, the blocksneed not correspond to physically distinct components. To the extentthat physically distinct components are used, connections betweencomponents (e.g., for data communication) can be wired and/or wirelessas desired.

An example of a technique for motion capture using the system of FIGS. 1and 2 will now be described. In this embodiment, cameras 102, 104 areoperated to collect a sequence of images of an object 108. The imagesare time correlated such that an image from camera 102 can be pairedwith an image from camera 104 that was captured at the same time (withina few milliseconds). These images are then analyzed, e.g., using mocapprogram 214, to determine the object's position and shape in 3D space.In some embodiments, the analysis considers a stack of 2D cross-sectionsthrough the 3D spatial field of view of the cameras. Thesecross-sections are referred to herein as “slices.”

FIGS. 3A and 3B are conceptual illustrations of how slices are definedin a field of view according to an embodiment of the present invention.FIG. 3A shows, in top view, cameras 102 and 104 of FIG. 1. Camera 102defines a vantage point 302, and camera 104 defines a vantage point 304.Line 306 joins vantage points 302 and 304. FIG. 3B shows a side view ofcameras 102 and 104; in this view, camera 104 happens to be directlybehind camera 102 and thus occluded; line 306 is perpendicular to theplane of the drawing. (It should be noted that the designation of theseviews as “top” and “side” is arbitrary; regardless of how the camerasare actually oriented in a particular setup, the “top” view can beunderstood as a view looking along a direction normal to the plane ofthe cameras, while the “side” view is a view in the plane of thecameras.)

An infinite number of planes can be drawn through line 306. A “slice”can be any one of those planes for which at least part of the plane isin the field of view of cameras 102 and 104. Several slices 308 areshown in FIG. 3B. (Slices 308 are seen edge-on; it is to be understoodthat they are 2D planes and not 1-D lines.) For purposes of motioncapture analysis, slices can be selected at regular intervals in thefield of view. For example, if the received images include a fixednumber of rows of pixels (e.g., 1080 rows), each row can be a slice, ora subset of the rows can be used for faster processing. Where a subsetof the rows is used, image data from adjacent rows can be averagedtogether, e.g., in groups of 2-3.

FIGS. 4A-4C illustrate an analysis that can be performed on a givenslice. FIG. 4A is a top view of a slice as defined above, correspondingto an arbitrary cross-section 402 of an object. Regardless of theparticular shape of cross-section 402, the object as seen from a firstvantage point 404 has a “left illuminated edge” point 406 and a “rightilluminated edge” point 408. As seen from a second vantage point 410,the same object has a “left illuminated edge” point 412 and a “rightilluminated edge” point 414. These are in general different points onthe boundary of object 402. A tangent line can be defined that connectseach illuminated edge point and the associated vantage point. Forexample, FIG. 4A also shows that tangent line 416 can be defined throughvantage point 404 and left illuminated edge point 406; tangent line 418through vantage point 404 and right illuminated edge point 408; tangentline 420 through vantage point 410 and left illuminated edge point 412;and tangent line 422 through vantage point 410 and right illuminatededge point 414.

It should be noted that all points along any one of tangent lines 416,418, 420, 422 will project to the same point on an image plane.Therefore, for an image of the object from a given vantage point, a leftilluminated edge point and a right illuminated edge point can beidentified in the image plane and projected back to the vantage point,as shown in FIG. 4B, which is another top view of a slice, showing theimage plane for each vantage point. Image 440 is obtained from vantagepoint 442 and shows left illuminated edge point 446 and rightilluminated edge point 448. Image 450 is obtained from vantage point 452and shows left illuminated edge point 456 and right illuminated edgepoint 458. Tangent lines 462, 464, 466, 468 can be defined as shown.Given the tangent lines of FIG. 4B, the location in the slice of anelliptical cross-section can be determined, as illustrated in FIG. 4C,where ellipse 470 has been fit to tangent lines 462, 464, 466, 468 ofFIG. 4B.

In general, as shown in FIG. 5, an ellipse in the xy plane can becharacterized by five parameters: the x and y coordinates of the center(x_(C), y_(C)), the semimajor axis (a), the semiminor axis (b), and arotation angle (θ) (e.g., the angle of the semimajor axis relative tothe x axis). With only four tangents, as is the case in FIG. 4C, theellipse is underdetermined. However, an efficient process for estimatingthe ellipse in spite of this has been developed. In various embodimentsas described below, this involves making an initial working assumption(or “guess”) as to one of the parameters and revisiting the assumptionas additional information is gathered during the analysis. Thisadditional information can include, for example, physical constraintsbased on properties of the cameras and/or the object.

In some embodiments, more than four tangents to an object may beavailable for some or all of the slices, e.g., because more than twovantage points are available. An elliptical cross-section can still bedetermined, and the process in some instances is somewhat simplified asthere is no need to assume a parameter value. In some instances, theadditional tangents may create additional complexity. Examples ofprocesses for analysis using more than four tangents are described belowand in the '554 application noted above.

In some embodiments, fewer than four tangents to an object may beavailable for some or all of the slices, e.g., because an edge of theobject is out of range of the field of view of one camera or because anedge was not detected. A slice with three tangents can be analyzed. Forexample, using two parameters from an ellipse fit to an adjacent slice(e.g., a slice that had at least four tangents), the system of equationsfor the ellipse and three tangents is sufficiently determined that itcan be solved. As another option, a circle can be fit to the threetangents; defining a circle in a plane requires only three parameters(the center coordinates and the radius), so three tangents suffice tofit a circle. Slices with fewer than three tangents can be discarded orcombined with adjacent slices.

In some embodiments, each of a number of slices is analyzed separatelyto determine the size and location of an elliptical cross-section of theobject in that slice. This provides an initial 3D model (specifically, astack of elliptical cross-sections), which can be refined by correlatingthe cross-sections across different slices. For example, it is expectedthat an object's surface will have continuity, and discontinuousellipses can accordingly be discounted. Further refinement can beobtained by correlating the 3D model with itself across time, e.g.,based on expectations related to continuity in motion and deformation.

A further understanding of the analysis process can be had by referenceto FIGS. 6A-6B, which provide a flow diagram of a motion-capture process600 according to an embodiment of the present invention. Process 600 canbe implemented, e.g., in mocap program 214 of FIG. 2.

At block 602, a set of images—e.g., one image from each camera 102, 104of FIG. 1—is obtained. In some embodiments, the images in a set are alltaken at the same time (or within a few milliseconds), although aprecise timing is not required. The techniques described herein forconstructing an object model assume that the object is in the same placein all images in a set, which will be the case if images are taken atthe same time. To the extent that the images in a set are taken atdifferent times, motion of the object may degrade the quality of theresult, but useful results can be obtained as long as the time betweenimages in a set is small enough that the object does not move far, withthe exact limits depending on the particular degree of precisiondesired.

At block 604, each slice is analyzed. FIG. 6B illustrates a per-sliceanalysis that can be performed at block 604. Referring to FIG. 6B, atblock 606, illuminated edge points of the object in a given slice areidentified in each image in the set. For example, edges of an object inan image can be detected using conventional techniques, such as contrastbetween adjacent pixels or groups of pixels. In some embodiments, if noilluminated edge points are detected for a particular slice (or if onlyone illuminated edge point is detected), no further analysis isperformed on that slice. In some embodiments, edge detection can beperformed for the image as a whole rather than on a per-slice basis.

At block 608, assuming enough illuminated edge points were identified, atangent line from each illuminated edge point to the correspondingvantage point is defined, e.g., as shown in FIG. 4C and described above.At block 610 an initial assumption as to the value of one of theparameters of an ellipse is made, to reduce the number of freeparameters from five to four. In some embodiments, the initialassumption can be, e.g., the semimajor axis (or width) of the ellipse.Alternatively, an assumption can be made as to eccentricity (ratio ofsemimajor axis to semiminor axis), and that assumption also reduces thenumber of free parameters from five to four. The assumed value can bebased on prior information about the object. For example, if previoussequential images of the object have already been analyzed, it can beassumed that the dimensions of the object do not significantly changefrom image to image. As another example, if it is assumed that theobject being modeled is a particular type of object (e.g., a hand), aparameter value can be assumed based on typical dimensions for objectsof that type (e.g., an average cross-sectional dimension of a palm orfinger). An arbitrary assumption can also be used, and any assumptioncan be refined through iterative analysis as described below.

At block 612, the tangent lines and the assumed parameter value are usedto compute the other four parameters of an ellipse in the plane. Forexample, as shown in FIG. 7, four tangent lines 701, 702, 703, 704define a family of inscribed ellipses 706 including ellipses 706 a, 706b, and 706 c, where each inscribed ellipse 706 is tangent to all four oflines 701-704. Ellipse 706 a and 706 b represent the “extreme” cases(i.e., the most eccentric ellipses that are tangent to all four of lines701-704. Intermediate between these extremes are an infinite number ofother possible ellipses, of which one example, ellipse 706 c, is shown(dashed line).

The solution process selects one (or in some instances more than one) ofthe possible inscribed ellipses 706. In one embodiment, this can be donewith reference to the general equation for an ellipse shown in FIG. 8.The notation follows that shown in FIG. 5, with (x, y) being thecoordinates of a point on the ellipse, (x_(C), y_(C)) the center, a andb the axes, and θ the rotation angle. The coefficients C₁, C₂ and C₃ aredefined in terms of these parameters, as shown in FIG. 8.

The number of free parameters can be reduced based on the observationthat the centers (x_(C), y_(C)) of all the ellipses in family 706 lineon a line segment 710 (also referred to herein as the “centerline”)between the center of ellipse 706 a (shown as point 712 a) and thecenter of ellipse 706 b (shown as point 712 b). FIG. 9 illustrates how acenterline can be found for an intersection region. Region 902 is a“closed” intersection region; that is, it is bounded by tangents 904,906, 908, 910. The centerline can be found by identifying diagonal linesegments 912, 914 that connect the opposite corners of region 902,identifying the midpoints 916, 918 of these line segments, andidentifying the line segment 920 joining the midpoints as thecenterline.

Region 930 is an “open” intersection region; that is, it is onlypartially bounded by tangents 904, 906, 908, 910. In this case, only onediagonal, line segment 932, can be defined. To define a centerline forregion 930, centerline 920 from closed intersection region 902 can beextended into region 930 as shown. The portion of extended centerline920 that is beyond line segment 932 is centerline 940 for region 930. Ingeneral, for any given set of tangent lines, both region 902 and region930 can be considered during the solution process. (Often, one of theseregions is outside the field of view of the cameras and can be discardedat a later stage.) Defining the centerline reduces the number of freeparameters from five to four because y_(C) can be expressed as a(linear) function of x_(C) (or vice versa), based solely on the fourtangent lines. However, for every point (x_(C), y_(C)) on thecenterline, a set of parameters {θ, a, b} can be found for an inscribedellipse. To reduce this to a set of discrete solutions, an assumedparameter value can be used. For example, it can be assumed that thesemimajor axis a has a fixed value a₀. Then, only solutions {θ, a, b}that satisfy a=a₀ are accepted.

In one embodiment, the ellipse equation of FIG. 8 is solved for θ,subject to the constraints that: (1) (x_(C), y_(C)) must lie on thecenterline determined from the four tangents (i.e., either centerline920 or centerline 940 of FIG. 9); and (2) a is fixed at the assumedvalue a₀. The ellipse equation can either be solved for θ analyticallyor solved using an iterative numerical solver (e.g., a Newtonian solveras is known in the art). An analytic solution can be obtained by writingan equation for the distances to the four tangent lines given a y_(C)position, then solving for the value of y_(C) that corresponds to thedesired radius parameter a=a₀. One analytic solution is illustrated inthe equations of FIGS. 10A-10D. Shown in FIG. 10A are equations for fourtangent lines in the xy plane (the slice). Coefficients A_(i), B_(i) andD_(i) (for i=1 to 4) can be determined from the tangent lines identifiedin an image slice as described above. FIG. 10B illustrates thedefinition of four column vectors r₁₂, r₂₃, r₁₄ and r₂₄ from thecoefficients of FIG. 10A. The “\” operator here denotes matrix leftdivision, which is defined for a square matrix M and a column vector vsuch that M\v=r, where r is the column vector that satisfies Mr=v. FIG.10C illustrates the definition of G and H, which are four-componentvectors from the vectors of tangent coefficients A, B and D and scalarquantities p and q, which are defined using the column vectors r₁₂, r₂₃,r₁₄ and r₂₄ from FIG. 10B.

FIG. 10D illustrates the definition of six scalar quantities v_(A2),v_(AB), v_(B2), w_(A2), w_(AB), and w_(B2) in terms of the components ofvectors G and H of FIG. 10C.

Using the parameters defined in FIGS. 10A-10D, solving for θ isaccomplished by solving the eighth-degree polynomial equation shown inFIG. 10E for t, where the coefficients Q_(i) (for i=0 to 8) are definedas shown in FIGS. 10F-10N. The parameters A₁, B₁, G₁, H₁, v_(A2),v_(AB), v_(B2), w_(A2), w_(AB), and w_(B2) used in FIGS. 10F-10N aredefined as shown in FIGS. 10A-10D. The parameter n is the assumedsemimajor axis (in other words, a₀). Once the real roots t are known,the possible values of θ are defined as θ=a tan(t).

As it happens, the equation of FIGS. 10E-10N has at most three realroots; thus, for any four tangent lines, there are at most threepossible ellipses that are tangent to all four lines and satisfy thea=a₀ constraint. (In some instances, there may be fewer than three realroots.) For each real root θ, the corresponding values of (x_(C), y_(C))and b can be readily determined. Depending on the particular inputs,zero or more solutions will be obtained; for example, in some instances,three solutions can be obtained for a typical configuration of tangents.Each solution is completely characterized by the parameters {θ, a=a₀, b,(x_(C), y_(C))}.

Referring again to FIG. 6B, at block 614, the solutions are filtered byapplying various constraints based on known (or inferred) physicalproperties of the system. For example, some solutions would place theobject outside the field of view of the cameras, and such solutions canreadily be rejected. As another example, in some embodiments, the typeof object being modeled is known (e.g., it can be known that the objectis or is expected to be a human hand). Techniques for determining objecttype are described below; for now, it is noted that where the objecttype is known, properties of that object can be used to rule outsolutions where the geometry is inconsistent with objects of that type.For example, human hands have a certain range of sizes and expectedeccentricities in various cross-sections, and such ranges can be used tofilter the solutions in a particular slice. These constraints can berepresented in any suitable format, e.g., a physical model (as describedbelow), an ordered list of parameters based on such a model, etc.

In some embodiments, cross-slice correlations can also be used to filter(or further filter) the solutions obtained at block 612. For example, ifthe object is known to be a hand, constraints on the spatialrelationship between various parts of the hand (e.g., fingers have alimited range of motion relative to each other and/or to the palm of thehand) as represented in a physical model or explicit set of constraintparameters can be used to constrain one slice based on results fromother slices. For purposes of cross-slice correlations, it should benoted that, as a result of the way slices are defined, the variousslices may be tilted relative to each other, e.g., as shown in FIG. 3B.Accordingly, each planar cross-section can be further characterized byan additional angle ø, which can be defined relative to a referencedirection 310 as shown in FIG. 3B.

At block 616, it is determined whether a satisfactory solution has beenfound. Various criteria can be used to assess whether a solution issatisfactory. For instance, if a unique solution is found (afterfiltering), that solution can be accepted, in which case process 600proceeds to block 620 (described below). If multiple solutions remain orif all solutions were rejected in the filtering at block 614, it may bedesirable to retry the analysis. If so, process 600 can return to block610, allowing a change in the assumption used in computing theparameters of the ellipse.

Retrying can be triggered under various conditions. For example, in someinstances, 30 the initial parameter assumption (e.g., a=a₀) may produceno solutions or only nonphysical solutions (e.g., object outside thecameras' field of view). In this case, the analysis can be retried witha different assumption. In one embodiment, a small constant (which canbe positive or negative) is added to the initial assumed parameter value(e.g., a₀) and the new value is used to generate a new set of solutions.This can be repeated until an acceptable solution is found (or until theparameter value reaches a limit). An alternative approach is to keep thesame assumption but to relax the constraint that the ellipse be tangentto all four lines, e.g., by allowing the ellipse to be nearly but notexactly tangent to one or more of the lines. (In some embodiments, thisrelaxed constraint can also be used in the initial pass through theanalysis.)

It should be noted that in some embodiments, multiple ellipticalcross-sections may be found in some or all of the slices. For example,in some planes, a complex object (e.g., a hand) may have a cross-sectionwith multiple disjoint elements (e.g., in a plane that intersects thefingers). Ellipse-based reconstruction techniques as described hereincan account for such complexity; examples are described below. Thus, itis generally not required that a single ellipse be found in a slice, andin some instances, solutions entailing multiple ellipses may be favored.

For a given slice, the analysis of FIG. 6B yields zero or moreelliptical cross-sections. In some instances, even after filtering atblock 616, there may still be two or more possible solutions. Theseambiguities can be addressed in further processing as described below.

Referring again to FIG. 6A, the per-slice analysis of block 604 can beperformed for any number of slices, and different slices can be analyzedin parallel or sequentially, depending on available processingresources. The result is a 3D model of the object, where the model isconstructed by, in effect, stacking the slices. At block 620,cross-slice correlations are used to refine the model. For example, asnoted above, in some instances, multiple solutions may have been foundfor a particular slice. It is likely that the “correct” solution (i.e.,the ellipse that best corresponds to the actual position of the object)will correlate well with solutions in other slices, while any “spurious”solutions (i.e., ellipses that do not correspond to the actual positionof the object) will not. Uncorrelated ellipses can be discarded. In someembodiments where slices are analyzed sequentially, block 620 can beperformed iteratively as each slice is analyzed.

At block 622, the 3D model can be further refined, e.g., based on anidentification of the type of object being modeled. In some embodiments,a library of object types can be provided (e.g., as object library 230of FIG. 2). For each object type, the library can provide characteristicparameters for the object in a range of possible poses (e.g., in thecase of a hand, the poses can include different finger positions,different orientations relative to the cameras, etc.). Based on thesecharacteristic parameters, a reconstructed 3D model can be compared tovarious object types in the library. If a match is found, the matchingobject type is assigned to the model.

Once an object type is determined, the 3D model can be refined usingconstraints based on characteristics of the object type. For instance, ahuman hand would characteristically have five fingers (not six), and thefingers would be constrained in their positions and angles relative toeach other and to a palm portion of the hand. Any ellipses in the modelthat are inconsistent with these constraints can be discarded. In someembodiments, block 622 can include recomputing all or portions of theper-slice analysis (block 604) and/or cross-slice correlation analysis(block 620) subject to the type-based constraints. In some instances,applying type-based constraints may cause deterioration in accuracy ofreconstruction if the object is misidentified. (Whether this is aconcern depends on implementation, and type-based constraints can beomitted if desired.)

In some embodiments, object library 230 can be dynamically and/oriteratively updated. For example, based on characteristic parameters, anobject being modeled can be identified as a hand. As the motion of thehand is modeled across time, information from the model can be used torevise the characteristic parameters and/or define additionalcharacteristic parameters, e.g., additional poses that a hand maypresent.

In some embodiments, refinement at block 622 can also includecorrelating results of analyzing images across time. It is contemplatedthat a series of images can be obtained as the object moves and/orarticulates. Since the images are expected to include the same object,information about the object determined from one set of images at onetime can be used to constrain the model of the object at a later time.(Temporal refinement can also be performed “backward” in time, withinformation from later images being used to refine analysis of images atearlier times.)

At block 624, a next set of images can be obtained, and process 600 canreturn to block 604 to analyze slices of the next set of images. In someembodiments, analysis of the next set of images can be informed byresults of analyzing previous sets. For example, if an object type wasdetermined, type-based constraints can be applied in the initialper-slice analysis, on the assumption that successive images are of thesame object. In addition, images can be correlated across time, andthese correlations can be used to further refine the model, e.g., byrejecting discontinuous jumps in the object's position or ellipses thatappear at one time point but completely disappear at the next.

It will be appreciated that the motion capture process described hereinis illustrative and that variations and modifications are possible.Steps described as sequential may be executed in parallel, order ofsteps may be varied, and steps may be modified, combined, added oromitted. Different mathematical formulations and/or solution procedurescan be substituted for those shown herein. Various phases of theanalysis can be iterated, as noted above, and the degree to whichiterative improvement is used may be chosen based on a particularapplication of the technology. For example, if motion capture is beingused to provide real-time interaction (e.g., to control a computersystem), the data capture and analysis should be performed fast enoughthat the system response feels like real time to the user. Inaccuraciesin the model can be tolerated as long as they do not adversely affectthe interpretation or response to a user's motion. In otherapplications, e.g., where the motion capture data is to be used forrendering in the context of digital movie-making, an analysis with moreiterations that produces a more refined (and accurate) model may bepreferred. As noted above, an object being modeled can be a “complex”object and consequently may present multiple discrete ellipses in somecross-sections. For example, a hand has fingers, and a cross-sectionthrough the fingers may include as many as five discrete elements. Theanalysis techniques described above can be used to model complexobjects.

By way of example, FIGS. 11A-11C illustrate some cases of interest. InFIG. 11A, cross-sections 1102, 1104 would appear as distinct objects inimages from both of vantage points 1106, 1108. In some embodiments, itis possible to distinguish object from background; for example, in aninfrared image, a heat-producing object (e.g., living organisms) mayappear bright against a dark background. Where object can bedistinguished from background, tangent lines 1110 and 1111 can beidentified as a pair of tangents associated with opposite edges of oneapparent object while tangent lines 1112 and 1113 can be identified as apair of tangents associated with opposite edges of another apparentobject. Similarly, tangent lines 1114 and 1115, and tangent lines 1116and 1117 can be paired. If it is known that vantage points 1106 and 1108are on the same side of the object to be modeled, it is possible toinfer that tangent pairs 1110, 1111 and 1116, 1117 should be associatedwith the same apparent object, and similarly for tangent pairs 1112,1113 and 1114, 1115. This reduces the problem to two instances of theellipse-fitting process described above. If less information isavailable, an optimum solution can be determined by iteratively tryingdifferent possible assignments of the tangents in the slice in question,rejecting non-physical solutions, and cross-correlating results fromother slices to determine the most likely set of ellipses.

In FIG. 11B, ellipse 1120 partially occludes ellipse 1122 from bothvantage points. In some embodiments, it may or may not be possible todetect the “occlusion” edges 1124, 1126. If edges 1124 and 1126 are notdetected, the image appears as a single object and is reconstructed as asingle elliptical cross-section. In this instance, information fromother slices or temporal correlation across images may reveal the error.If occlusion edges 1124 and/or 1126 are visible, it may be apparent thatthere are multiple objects (or that the object has a complex shape) butit may not be apparent which object or object portion is in front. Inthis case, it is possible to compute multiple alternative solutions, andthe optimum solution may be ambiguous. Spatial correlations acrossslices, temporal correlations across image sets, and/or physicalconstraints based on object type can be used to resolve the ambiguity.

In FIG. 11C, ellipse 1140 fully occludes ellipse 1142. In this case, theanalysis described above would not show ellipse 1142 in this particularslice. However, spatial correlations across slices, temporalcorrelations across image sets, and/or physical constraints based onobject type can be used to infer the presence of ellipse 1142, and itsposition can be further constrained by the fact that it is apparentlyoccluded. In some embodiments, multiple discrete cross-sections (e.g.,in any of FIGS. 11A-11C) can also be resolved using successive imagesets across time. For example, the four-tangent slices for successiveimages can be aligned and used to define a slice with 5-8 tangents. Thisslice can be analyzed using techniques described below.

In one embodiment of the present invention, a motion capture system canbe used to detect the 3D position and movement of a human hand. In thisembodiment, two cameras are arranged as shown in FIG. 1, with a spacingof about 1.5 cm between them. Each camera is an infrared camera with animage rate of about 60 frames per second and a resolution of 640×480pixels per frame. An infrared light source (e.g., an IR light-emittingdiode) that approximates a point light source is placed between thecameras to create a strong contrast between the object of interest (inthis case, a hand) and background. The falloff of light with distancecreates a strong contrast if the object is a few inches away from thelight source while the background is several feet away.

The image is analyzed using contrast between adjacent pixels to detectedges of the object. Bright pixels (detected illumination above athreshold) are assumed to be part of the object while dark pixels(detected illumination below a threshold) are assumed to be part of thebackground. Edge detection may take approximately 2 ms with conventionalprocessing capability. The edges and the known camera positions are usedto define tangent lines in each of 480 slices (one slice per row ofpixels), and ellipses are determined from the tangents using theanalytical technique described above with reference to FIGS. 6A and 6B.In a typical case of modeling a hand, roughly 800-1200 ellipses aregenerated from a single pair of image frames (the number depends on theorientation and shape of the hand) within, in various embodiments, about6 ms. The error in modeling finger position in one embodiment is lessthan 0.1 mm.

FIG. 12 illustrates a model 1200 of a hand that can be generated usingthe system just described. As can be seen, the model does not have theexact shape of a hand, but a palm 1202, thumb 1204 and four fingers 1206can be clearly recognized. Such models can be useful as the basis forconstructing more realistic models. For example, a skeleton model for ahand can be defined, and the positions of various joints in the skeletonmodel can be determined by reference to model 1200. Using the skeletonmodel, a more realistic image of a hand can be rendered. Alternatively,a more realistic model may not be needed. For example, model 1200accurately indicates the position of thumb 1204 and fingers 1206, and asequence of models 1200 captured across time will indicate movement ofthese digits. Thus, gestures can be recognized directly from model 1200.The point is that ellipses identified and tracked as described above canbe used to drive visual representations of the object tracked byapplication to a physical model of the object. The model may be selectedbased on a desired degree of realism, the response time desired (or thelatency that can be tolerated), and available computational resources.

It will be appreciated that this example system is illustrative and thatvariations and modifications are possible. Different types andarrangements of cameras can be used, and appropriate image analysistechniques can be used to distinguish object from background and therebydetermine a silhouette (or a set of edge locations for the object) thatcan in turn be used to define tangent lines to the object in various 2Dslices as described above. Given four tangent lines to an object, wherethe tangents are associated with at least two vantage points, anelliptical cross-section can be determined; for this purpose it does notmatter how the tangent lines are determined. Thus, a variety of imagingsystems and techniques can be used to capture images of an object thatcan be used for edge detection. In some cases, more than four tangentscan be determined in a given slice. For example, more than two vantagepoints can be provided.

In one alternative embodiment, three cameras can be used to captureimages of an object. FIG. 13 is a simplified system diagram for a system1300 with three cameras 1302, 1304, 1306 according to an embodiment ofthe present invention. Each camera 1302, 1304, 1306 provides a vantagepoint 1308, 1310, 1312 and is oriented toward an object of interest1313. In this embodiment, cameras 1302, 1304, 1306 are arranged suchthat vantage points 1308, 1310, 1312 lie in a single line 1314 in 3Dspace. Two-dimensional slices can be defined as described above, exceptthat all three vantage points 1308, 1310, 1312 are included in eachslice. The optical axes of cameras 1302, 1304, 1306 can be but need notbe aligned, as long as the locations of vantage points 1308, 1310, 1312are known. With three cameras, six tangents to an object can beavailable in a single slice. FIG. 14 illustrates a cross-section 1402 ofan object as seen from vantage points 1308, 1310, 1312. Lines 1408,1410, 1412, 1414, 1416, 1418 are tangent lines to cross-section 1402from vantage points 1308, 1310, 1312, respectively.

For any slice with five or more tangents, the parameters of an ellipseare fully determined, and a variety of techniques can be used to fit anelliptical cross-section to the tangent lines. FIG. 15 illustrates onetechnique, relying on the “centerline” concept illustrated above in FIG.9. From a first set of four tangents 1502, 1504, 1506, 1508 associatedwith a first pair of vantage points, a first intersection region 1510and corresponding centerline 1512 can be determined. From a second setof four tangents 1504, 1506, 1514, 1516 associated with a second pair ofvantage points, a second intersection region 1518 and correspondingcenterline 1520 can be determined. The ellipse of interest 1522 shouldbe inscribed in both intersection regions. The center of ellipse 1522 istherefore the intersection point 1524 of centerlines 1512 and 1520. Inthis example, one of the vantage points (and the corresponding twotangents 1504, 1506) are used for both sets of tangents. Given more thanthree vantage points, the two sets of tangents could be disjoint ifdesired.

Where more than five tangent points (or other points on the object'ssurface) are available, the elliptical cross-section is mathematicallyoverdetermined. The extra information can be used to refine theelliptical parameters, e.g., using statistical criteria for a best fit.In other embodiments, the extra information can be used to determine anellipse for every combination of five tangents, then combine theelliptical contours in a piecewise fashion. Alternatively, the extrainformation can be used to weaken the assumption that the cross-sectionis an ellipse and allow for a more detailed contour. For example, acubic closed curve can be fit to five or more tangents.

In some embodiments, data from three or more vantage points is usedwhere available, and four-tangent techniques (e.g., as described above)can be used for areas that are within the field of view of only two ofthe vantage points, thereby expanding the spatial range of amotion-capture system.

While thus far the invention has been described with respect to specificembodiments, one skilled in the art will recognize that numerousmodifications are possible. The techniques described above can be usedto reconstruct objects from as few as four tangent lines in a slice,where the tangent lines are defined between edges of a projection of theobject onto a plane and two different vantage points. Thus, for purposesof the analysis techniques described herein, the edges of an object inan image are of primary significance. Any image or imaging system thatsupports determining locations of edges of an object in an image planecan therefore be used to obtain data for the analysis described herein.

For instance, in embodiments described above, the object is projectedonto an image plane using two different cameras to provide the twodifferent vantage points, and the illuminated edge points are defined inthe image plane of each camera. However, those skilled in the art withaccess to the present disclosure will appreciate that it may be possibleto use a single camera to capture motion and/or determine the shape andposition of the object in 3D space.

One skilled in the art with access to the present disclosure willappreciate that it is possible to use more or fewer than two cameras tocapture motion and/or determine the shape and position of the object in3D space. Referring to FIG. 16A, in some embodiments, the motion-capturesystem 1600 includes a single camera 1602. A cross-section 1604 of theobject as described above may be fit to an ellipse or any other simpleclosed curve. If an ellipse is used, the ellipse can be characterized byfive parameters, namely, the x and y coordinates of the ellipticalcenter (x_(C), y_(C)), the semimajor axis (a), the semiminor axis (b),and a rotation angle (θ) (e.g., the angle of the semimajor axis relativeto the x axis); five equations specify the five characteristicparameters, thereby identifying the ellipse. In various embodiments, thesingle camera 1602 has a vantage point 1606 that can detect two lightrays 1608, 1610 transmitted from a left-edge tangent point 1612 and aright-edge tangent point 1614, respectively, on the cross-section 1604.The two tangent points 1612, 1614 define a viewed portion 1616 of thecross-section 1604 within which the portion of the cross-section iswithin the field of view of the camera. The two tangent points 1612,1614 provide two equations that can partially determine the ellipse 1618that fits most closely to the cross-section 1604.

FIG. 16B illustrates a motion-capture system 1600 that includes threelight sources (e.g., LEDs) 1620, 1622, 1624 to illuminate the object andprovide additional information about the cross-section 1604 to determinethe parameters of the ellipse. In one embodiment, depending on therelative positions between the object, the camera 1602, and the lightsources 1620, 1622, 1624, the camera 1602 detects shadow (e.g.,unilluminated) regions on the cross-section 1604 created by the lightsources 1620, 1622, 1624. For example, the light source 1620 illuminatesa partial portion 1626 of the cross-section 1604; the illuminatedportion 1626 is determined by the position of the light source 1620 andtwo illuminated edge points 1628, 1630. For example, the two illuminatededge points 1628, 1630 may be defined by the light rays 1632, 1634tangent to the cross-section 1604. As a result, a shadow (orunilluminated) region 1636 that has limited exposure to the lightillumination from the light source 1620 can be observed on thecross-section 1604.

Because the viewed portion of the cross-section 1604 within the camera'sfield of view is defined by the two tangent points 1612, 1614, thecamera 1602 can detect the illuminated part 1638 between the tangentpoints 1612 and 1628 and the shadow region 1640 between the tangentpoints 1628 and 1614. Accordingly, the boundary between the shadowregion 1640 and the illuminated part 1638 defines a shadow edge point1628. In various embodiments, the shadow edge point 1628 is detected bythe camera 1602; the detected shadow point 1628 can provide twoadditional equations that further determine the characteristic ellipseparameters. The first equation is based on the detected position of theshadow edge point 1628, and the second equation is based on a light ray1642 emitted from the light source 1620 to the shadow edge point 1628.In one embodiment, the path of the light ray 1642 is based on thespatial relationship between the camera 1602 and the light source 1616.Although the detected shadow edge point 1628 provides two additionalequations to determine the characteristic parameters of the ellipse, theshadow edge point 1628 introduces an additional unknown parameter (e.g.the distance between the camera 1602 and the shadow edge point 1628).

FIG. 16C shows how multiple light sources 1620, 1622, 1624 illuminatethe cross-section 1604 and generate multiple shadow regions 1644, 1646,1648, respectively. Shadow edge points 1628, 1650, 1652 definingboundaries between the shadow regions 1644, 1646, 1648 and theilluminated regions are detected by the camera 1602. As described above,each detected shadow edge point 1628, 1650, 1652 can provide twoadditional equations that contribute to determining the characteristicellipse parameters. In addition, each detected shadow edge point 1628,1650, 1652 may also introduce an additional unknown parameter (e.g. thedistance between the camera 1602 and the corresponding shadow edgepoint). As a result, utilizing three light sources 1620, 1622, 1624creates three additional unknown parameters and provides six equationsto determine the characteristic the ellipse parameters.

In summary, when the motion-capture system 1600 includes three lightsources 1620, 1622, 1624, each creating a shadow edge point on thecross-section 1604 of the object, eight unknown parameters—including thefive characteristic parameters of the ellipse and the three distancesfrom the camera 1602 to the three shadow edge points 1628, 1646,1656—are solved to determine the position, rotation, and size of theellipse. In various embodiments, the camera 1602 detects two tangentpoints 1612, 1614 on the object cross-section that provide two equationsto partially determine the eight unknown parameters and the three shadowedge points 1628, 1646, 1656 created by light emitted from the lightsources 1620, 1622, 1624 onto the cross-section 1604 of the object.Because each shadow edge point 1628, 1646, 1656 provides two equations,the motion-capture system 1600 thus has eight equations to solve for theeight unknown parameters, including five unknown ellipse parameters andthe three unknown distances introduced by the three shadow edge points1628, 1646, 1656.

In some embodiments, the motion-capture system 1600 includes fewer thanthree light sources, such as two light sources 1620, 1622. The two lightsources 1620, 1622 create two unknown parameters (i.e., the distancebetween the camera and the shadow edge points generated by the lightsources 1620, 1622) and four equations (i.e., the two positions of theshadow edge points and the two light rays emitted from the light sources1620, 1622 to the shadow edge points). Accordingly, the motion-capturesystem 1600 has, in total, seven unknown parameters and six equations,so the ellipse is underdetermined. Because the six equations bythemselves cannot have an exact solution for the seven unknownparameters, in one embodiment, one of the seven unknown parameters isinitially estimated. The estimated parameter is then applied to the sixequations, and the other six unknown parameters can be solved. In oneembodiment, the self-consistency of the estimated parameter and the sixsolved parameters is checked in the end of the process to determine theaccuracy of the estimated parameter. This process may iterate until amaximum self-consistency or accuracy of the estimated parameter isobtained.

In some embodiments, there are more than three light sources, yieldingmore available equations than unknown parameters, and the ellipse isoverdetermined. The extra equations may be utilized to refine theelliptical parameters, e.g., using statistical criteria for a best fit.Alternatively, the extra information can be used to weaken theassumption that the cross-section is an ellipse and allow for a moredetailed contour. For example, a cubic closed curve can be fit to thetwo tangent points and the three shadow points. In some embodiments, theextra equations may be used to optimize the speed and/or accuracy of anumerical solver that is utilized to solve the unknown parameters and isimplemented on a general-purpose computing device.

In some embodiments, the light sources 1620, 1622, 1624 are pulsed onindividually and in succession, allowing for each of the shadow regions1644, 1646, 1648 and the shadow points 1628, 1650, 1652 to be associatedwith a single light source. In some embodiments, light sources 1616,1618, and 1620 may be of different wavelengths, allowing the shadow edgepoints 1628, 1650, 1652 to be easily identified.

Additionally, those skilled in the art with access to the presentdisclosure will appreciate that cameras are not the only tool capable ofprojecting an object onto an imaging surface. For example, a lightsource can create a shadow of an object on a target surface, and theshadow—captured as an image of the target surface—can provide aprojection of the object that suffices for detecting edges and definingtangent lines. The light source can produce light in any visible ornon-visible portion of the electromagnetic spectrum. Any frequency (orrange of frequencies) can be used, provided that the object of interestis opaque to such frequencies while the ambient environment in which theobject moves is not. The light sources used should be bright enough tocast distinct shadows on the target surface. Point-like light sourcesprovide sharper edges than diffuse light sources, but any type of lightsource can be used.

In one such embodiment, a single camera is used to capture images ofshadows cast by multiple light sources. FIG. 17 illustrates a system1700 for capturing shadows of an object according to an embodiment ofthe present invention. Light sources 1702 and 1704 illuminate an object1706, casting shadows 1708, 1710 onto a front side 1712 of a surface1714. Surface 1714 can be translucent so that the shadows are alsovisible on its back side 1716. A camera 1718 can be oriented toward backside 1716 as shown and can capture images of shadows 1708, 1710. Withthis arrangement, object 1706 does not occlude the shadows captured bycamera 1718. Light sources 1702 and 1704 define two vantage points, fromwhich tangent lines 1720, 1722, 1724, 1726 can be determined based onthe edges of shadows 1708, 1710. These four tangents can be analyzedusing techniques described above.

In an embodiment such as system 1700 of FIG. 17, shadows created bydifferent light sources may partially overlap, depending on where theobject is placed relative to the light source. In such a case, an imagemay have shadows with penumbra regions (where only one light source iscontributing to the shadow) and an umbra region (where the shadows fromboth light sources overlap). Detecting edges can include detecting thetransition from penumbra to umbra region (or vice versa) and inferring ashadow edge at that location. Since an umbra region will be darker thana penumbra region; contrast-based analysis can be used to detect thesetransitions.

Certain physical or object configurations may present ambiguities thatare resolved in accordance with various embodiments we as now discussed.Referring to FIG. 18, when two objects 1808, 1810 are present, thecamera 1820 may detect four shadows 1812, 1814, 1816, 1818 and thetangent lines may create four intersection regions 1822, 1824, 1826,1828 that all lie within the shadow regions 1830, 1832, 1834, 1836.Because it is difficult to determine, from a single slice of the shadowimage, which of these intersection regions contain portions of theobject, an analysis of whether the intersection regions 1822, 1824,1826, 1828 are occupied by the objects may be ambiguous. For example,shadows 1812, 1814, 1816, 1818 that are generated when intersectionregions 1822 and 1826 are occupied are the same as those generated whenregions 1824 and 1828 are occupied, or when all four intersectionregions 1822, 1824, 1826, 1828 are occupied. In one embodiment,correlations across slices are used to resolve the ambiguity ininterpreting the intersection regions (or “visual hulls”) 1822, 1824,1826, 1828.

In various embodiments, referring to FIG. 19, a system 1900 incorporatesa large number of light sources (i.e., more than two light sources) toresolve the ambiguity of the intersection regions when there aremultiple objects casting shadows. For example, the system 1900 includesthree light sources 1902, 1904, 1906 to cast light onto a translucentsurface 1910 and a camera 1912 positioned on the opposite side ofsurface 1910 to avoid occluding the shadows cast by an object 1914. Asshown in FIG. 19, because utilization of three light sources providesfive or more tangents for one or more objects 1914 in a slice, theellipse-fitting techniques described above may be used to determine thecross-sections of the objects. A collection of the cross-sections of theobjects in 2D slices may then determine the locations and/or movement ofthe objects.

If multiple objects, however, are located in close proximity (e.g., thefingers of a hand), utilization of additional light sources may reducethe sizes of the various intersection regions as well as increase thetotal number of intersection regions. If the number of light sources ismuch greater than the number of the proximal objects, the intersectionregions may be too small to be analyzed based on a known or assumed sizescale of the object. Additionally, the increased number of intersectionregions may result in more ambiguity in distinguishing intersectionregions that contain objects from intersection regions that do notcontain objects (i.e., “blind spots”). In various embodiments, whetheran intersection region contains an object is determined based on theproperties of a collection of intersection points therein. As describedin greater detail below, an intersection point is defined by at leasttwo shadow lines, each connecting a shadow point of the shadow and alight source. If the intersection points in an intersection regionsatisfy certain criteria, the intersection region is considered to havethe objects therein. A collection of the intersection regions may thenbe utilized to determine the shape and movement of the objects.

Referring to FIG. 20, a collection of the intersection regions (a visualhull) 2030 is defined by a virtual rubber band 2032 stretched aroundmultiple intersection regions 2031 (or “convex hulls”); eachintersection region 2031 is defined by a smallest set of intersectionpoints 2034. When there are multiple intersection regions 2031,distinguishing each intersection region 2031 from a collection ofintersection points 2034 may be difficult. In some embodiments,referring to FIG. 21, a simple visual hull is first constructed by asetup of two lights 2102, 2104 (here denoted Ln, with n={1, 2} to permitfurther generalization to greater numbers of light sources, shadows,shadow regions, points, and visual hulls), each casting one shadow2106A, 2106B, respectively. The light source L₁ and shadow 2106A definea shadow region, R_(1,1); similarly, light source L₂ and the shadow2106B define a shadow region, R_(2,1); in general, the shadow region isdenoted as, R_(u,v), where u is the number of the corresponding lightsource and v is a number that denotes a left to right ordering in ascene within the set of all shadow regions from the light source u.Boundaries of the shadows (or “shadow points”) lie on an x axis and aredenoted by S_(u,v). The shadow points and each light source may thencreate shadow lines 2108, 2110, 2112, 2114; the shadow lines arereferenced by the two connecting points; for example, L₁S_(1,2) ,(abbreviated S_(1,2) , where the first subscript also refers to thelight number). The convex hull 2130 (or visual hull here since there isonly one intersection region 2128) may then be defined by the fourintersection points 2134 in the example of FIG. 21. In one embodiment,the intersection points 2134 are determined based on the intersectionsof every pair of shadow lines, for example, S_(1,1) , S_(1,2) , S_(2,1)and S_(2,2) . Because pairs of shadow lines from the same light sourceL₁ or L₂ do not intersect, the intersection of the pairs of lines fromthe same light source may then be neglected.

When there are more than two light sources, determining all shadow lineintersections no longer suffices to find intersection points that lie onthe intersection region 2128. Referring to FIG. 22A, utilization ofthree light sources 2202, 2204, 2206, may result in “true” intersectionpoints 2234A, 2234B, 2234C, 2234D, 2234E, 2234F that form theintersection region 2228 occupied by the object 2208 and “false”intersection points 2235A, 2235B, 2235C, 2235D, 2235E, 2235F thatclearly do not form the intersection region 2228. For example, the falseintersection point 2235E created by a left shadow line 2224 of theshadow region 2218A and a right shadow line 2226 of the shadow region2218B is a false intersection point because it does not lie inside theintersection region 2228. Because the intersection region 2228 is anintersection of the shadow regions 2218A, 2218B, 2218C created by theobject 2208 and the light sources 2202, 2204, 2206, the number of shadowregions in which each “true” intersection point lies is equal to thenumber of the light sources (i.e., three in FIG. 22A). “False”intersection points, by contrast, lie outside the intersection region2228 even though they may lie inside an intersection region thatincludes fewer number of shadow regions compared to the total number oflight sources. In one embodiment, whether an intersection point is“true” or “false” is determined based on the number of shadow regionsincluded in the intersection region in which the intersection pointlies. For example, in the presence of three light sources in FIG. 22A,the intersection point 2234A is a true intersection point because itlies inside three shadow regions 2218A, 2218B, 2218C; whereas theintersection point 2235F is a false intersection point because it liesinside only two shadow regions 2218B, 2218C.

Because the intersection regions are defined by a collection ofintersection points, excessive computational effort may be required todetermine whether an intersection point is contained by a correct numberof regions (i.e., the number of the light sources). In some embodiments,this computational complexity is reduced by assuming that eachintersection point is not “false” and then determining whether theresults are consistent with all of the shadows captured by the camera.These configurations project each intersection point I=[I_(x),I_(y)]onto the x axis through a ray directed from each light sourceL=[L_(x),L_(y)] that is not involved in the original intersectiondetermination. The solutions for these projections are given by

$\left\lbrack {\frac{{L_{y}P_{x}} - {L_{x}P_{y}}}{L_{y} - P_{y}},0} \right\rbrack.$If a projection point on the x axis lies inside a shadow region from thetesting light source, it is likely that the projected intersection pointis a true intersection point. For example, referring to FIG. 22B, theintersection point 2235E is determined by the shadow lines 2224 and 2226created by the light sources 2202 and 2206. Projecting the intersectionpoint 2235E onto the x axis using the light source 2206, which is notinvolved in determining the intersection point 2235E, creates aprojection point P₃. Because the projection point P₃ does not lie insidethe shadow region 2218C created by the light source 2206 and the object2208, the intersection point 2235E is considered to be a falseintersection point; whereas the intersection point 2234E is a trueintersection point because the projection point P₁ thereof lies withinthe shadow region 2218A. As a result, for every possible intersectionpoint, an additional N−2 projections must be determined for the N−2light sources that are not involved in determining the position of theintersection point (where N is the total number of light sources in thesystem). In other words, a projection check must be made for every lightsource other than the original two that are used to determine the testedintersection point. Because determining whether the intersection pointis true or false based on the projections is simpler than checking thenumber of shadow regions in which each intersection point lies, therequired computational requirements and processing time may besignificantly reduced.

If, however, a large quantity of light sources is utilized in thesystem, the overall process may still be time-consuming. In variousembodiments, the light sources L₁, L₂, and L₃ are placed in a lineparallel to the x axis, the location of the projection points can thenbe determined without finding the location of the intersection point forevery pair of shadow lines. Accordingly, whether the intersection point2234 is a true or false point may be determined without finding orlocating the position thereof; this further reduces the processing time.For example, with reference to FIG. 22C, assuming that the shadow pointsS₁ and S₃ are either known or have been determined, whether theintersection point I of the shadow lines L₁S₃ and L₃S₁ is true or falsemay be determined by the position of the projection point P₂ created bythe light source L₂. The distance between the projection point P₂created by the light source L₂ and the shadow point S₁ is given as:

$\begin{matrix}{\overset{\_}{S_{1}P_{2}} = {\overset{\_}{S_{1}S_{3}}\begin{bmatrix}\overset{\_}{L_{2}L_{3}} \\\overset{\_}{L_{1}L_{3}}\end{bmatrix}}} & \left( {{Eq}.\mspace{14mu} 1} \right)\end{matrix}$Thus, the location of any one of the projection points projected fromthe intersection point, I, and light sources may be determined based onthe other two shadow points and the distance ratios associated withlight sources L₁, L₂ and L₃. Because the ratio of the distances betweenthe light sources is predetermined, the complexity in determining theprojection point P₂ is reduced to little more than calculating distancesbetween the shadow points and multiplying these distances by thepredetermined ratio. If the distance between the projection point P₂ andthe shadow point S₁ is larger than the size of the shadow, i.e., S₁S₃ ,that is captured by the camera, the intersection point, I, is a falsepoint. If, on the other hand, the distance between the projection pointsS₂ and S₁ is smaller than the size of the shadow, the intersection pointI is likely a true point. Although the location of the intersectionpoint, I, may still be determined based on the shadow lines L₁S₃ andL₃S₁ , this determination may be skipped during the process.Accordingly, by aligning the light sources in a line, the falseintersection points can be quickly determined without performing thecomplex computations, thereby saving a large amount of processing timeand power.

More generally, when there are N light sources, each denoted as L_(i)(1≦i≧N), arranged on a line parallel to the x axis and each light sourcepossesses a set of S_(i) shadow points (where i is the light number), atotal number of M intersection calculations for all possibleintersection pairs is given as:

$\begin{matrix}{M = {\sum\limits_{i = 1}^{N - 1}{{S_{i}\left( {\sum\limits_{k = {i + 1}}^{N}S_{k}} \right)}.}}} & \left( {{Eq}.\mspace{14mu} 2} \right)\end{matrix}$For example, if there are N light sources, each casting n shadows, thetotal number of intersection calculations M may then be given asM=n ² N(N−1).  (Eq. 3)Because each of these intersection calculations involves multipleoperations (e.g., addition and multiplication), the total number ofoperations, T_(o), may be given asT _(o)=2n ² N(2N+1)(N−1).  (Eq. 4)For example, a total number of operations T_(o)=2(1)²3(2·3+1)(3−1)=84 isrequired to determine the simplest visual hull 2128 shown in FIG. 21. Inone embodiment, there are, for example, 12 light sources (i.e., N=12),each casting 10 shadows (i.e., n=10); the number of requiredintersection calculations for this scenario is M=13,200, setting thenumber of total operations to be T_(o)=660,000. Again, this requires asignificant amount of processing time. In some embodiments, the distanceratios between light sources are predetermined, and as a result, onlyone operation (i.e., multiplication) is needed to determine which pairsof shadow points produce true intersection points; this reduces thenumber of total operations to 13,200.

The computational load required to find the visual hull depends on thequantity of the true intersection points, which may not be uniquelydetermined by the number of shadows. Suppose, for example, that thereare N light sources and each object is a circle that casts one shadowper light; this results in N intersection regions (or 6N intersectionpoints) per object. Because there are n objects, the resulting number ofintersection points that need to be checked is 6Nn² (i.e., roughly 6,000for 10 objects cast by 12 light sources). As described above, the numberof operations required for the projection check is 13,200; accordingly,a total number of operations 19,200 is necessary to determine the visualhull formed by the true intersection points. This is a 34-foldimprovement in determining the solution for a single 2D scene comparedto the previous estimate of 660,000 operations. The number of reducedoperations may be given as:T _(P) =n ² N(N−1)+6Nn ²  (Eq. 5)The ratio of the required operations to the reduced operations may thenbe expressed as:

$\begin{matrix}{\frac{T_{o}}{T_{p}} = \frac{2{n\left( {{2N} + 1} \right)}\left( {N - 1} \right)}{{nN} - n + {6n}}} & \left( {{Eq}.\mspace{14mu} 6} \right)\end{matrix}$Based on Eq. 6, if the light sources lie along a line or lines parallelto the x axis, the improvement is around an order of magnitude for asmall number of lights, whereas the improvement is nearly two orders ofmagnitude for a larger number of lights.

If the objects are reconstructed in 3D space and/or a fast real-timerefresh rate (e.g., 30 frames per second) is used by the camera, thecomputational load may be increased by several orders of magnitude dueto the additional complexity. In some embodiments, the visual hull issplit into a number of small intersection regions that can generate atleast a portion of the shadows in the scene; the smallest cardinality ofthe set of small intersection regions is defined as a “minimalsolution.” In one embodiment, the number of the small intersectionregions in the minimal solution is equal to the largest number ofshadows generated by any single light source. The computationalcomplexity of obtaining the visual hull may significantly be reduced bydetermining each of the small visual hulls prior to assembling themtogether into the visual hull.

Referring again to FIG. 20, the intersection points 2034 may form anamorphous cloud that does not imply particular regions. In variousembodiments, this cloud is first split into a number of sets, each setdetermining an associated convex hull 2031. As further described below,in one embodiment, a measure is utilized to determine the intersectionregion to which each intersection point belongs. The determinedintersection region may then be assembled into an exact visual hull. Inone implementation, the trivial case of a visual hull containing onlyone intersection region is ignored. In some embodiments, everyintersection region ρ is assigned an N-dimensional subscript, where N isthe number of light sources in the scene under consideration. The nthentry for this subscript of the intersection region ρ is defined as thevalue v of the uth subscript (where u=n) for each shadow region R_(u,v)of which the intersection region is a subset; every intersection regionthus has a unique identifier for grouping the intersection points, asshown in FIG. 23. Because two of the subscript entries for anintersection point can be determined directly from the two shadow lines,the resulting intersection point thereof is in the two shadow regions inwhich the shadow lines are located. For the rest of the entries, thelocations of the projections of the intersection points may be recordedduring the determination of true and false intersection points. Completeknowledge of the particular intersection regions for each intersectionpoint may thus be determined.

Once the distinct intersection regions have been determined, thesmallest subset of intersection regions that can generate all of thefinal shadows may then be found. FIG. 23 depicts intersection regionsρ_(1,1,1), ρ_(2,2,2), ρ_(3,3,3) resulting from casting light from threelight sources onto three objects 2338A, 2338B, and 2338C. Because thegreatest number of shadows cast by any particular light source in thiscase is three and the number of intersection regions in the minimalsolution is equal to the largest number of shadows generated by anysingle light source, every group that includes three intersectionregions in the scene may be tested. If a group generates a complete setof shadows captured by the camera, this group is the minimum solution.The number of trios to test is equal to the binomial coefficient

${C_{u}^{j} = {\begin{pmatrix}j \\u\end{pmatrix} = \frac{j!}{{u!}{\left( {j - u} \right)!}}}},$where j is the total number of intersection regions. For example, thereare C₃ ¹³=286 combinations in FIG. 23. The likelihood that a trio havinglarger intersection regions can generate all of the captured shadows ishigher than for a trio having smaller intersection regions;additionally, larger intersection regions usually have a greater numberof intersection points. In some embodiments, the number of trios testedis reduced by setting a criterion value U equal to the greatest numberof intersection points in any intersection region. For example, onlyregions or combinations of regions having a number of intersectionpoints exceeding the criteria number U are checked. If there are nosolutions, U may be reset to U−1 and the process may be repeated. Forexample, by setting U=6, there are only five regions, ρ_(1,1,1),ρ_(2,2,2), ρ_(3,3,3), ρ_(1,2,3), ρ_(3,2,1), having six intersectionpoints need to be checked. The region subscripts may be presented as asingle number vector, e.g., ρ_(1,1,1)=[1 1 1]; and the combination ofρ_(3,2,1), ρ_(1,1,1), and ρ_(2,2,2) may be written as a matrix, e.g.,

$\quad{\begin{bmatrix}3 & 2 & 1 \\1 & 1 & 1 \\2 & 2 & 2\end{bmatrix}.}$There are nine additional combinations exist in FIG. 23:

$\begin{bmatrix}3 & 2 & 1 \\1 & 1 & 1 \\3 & 3 & 3\end{bmatrix},\begin{bmatrix}3 & 2 & 1 \\1 & 1 & 1 \\1 & 2 & 3\end{bmatrix},\begin{bmatrix}3 & 2 & 1 \\2 & 2 & 2 \\3 & 3 & 3\end{bmatrix},\left\lbrack \begin{matrix}3 & 2 & 1 \\2 & 2 & 2 \\1 & 2 & 3\end{matrix} \right\rbrack,\left\lbrack \begin{matrix}3 & 2 & 1 \\3 & 3 & 3 \\1 & 2 & 3\end{matrix} \right\rbrack,\left\lbrack \begin{matrix}1 & 1 & 1 \\2 & 2 & 2 \\3 & 3 & 3\end{matrix} \right\rbrack,{\quad{\left\lbrack \begin{matrix}1 & 1 & 1 \\2 & 2 & 2 \\1 & 2 & 3\end{matrix} \right\rbrack,\begin{bmatrix}1 & 1 & 1 \\3 & 3 & 3 \\1 & 2 & 3\end{bmatrix},{\begin{bmatrix}2 & 2 & 2 \\3 & 3 & 3 \\1 & 2 & 3\end{bmatrix}.}}}$Because the minimal solution alone can generate all of the shadows inthe scene, each column of the minimal solution matrix has the numbers 1,2, 3 (in no particular order). Accordingly, the 6th combination abovehaving ρ_(1,1,1), ρ_(2,2,2), and ρ_(3,3,3) is the minimal solution. Thisapproach finds the minimal solution by determining whether there is atleast one intersection region in every shadow region. This approach,however, may be time-consuming upon reducing U to 3, as the regions thathave three intersection point require a more complicated check. In someembodiments, the three-point regions are neglected since they are almostnever a part of a minimal solution.

In some embodiments, the 3D scenes are decomposed into a number of 2Dscenes that can be quickly solved by the approaches as described aboveto determine the 3D shape of the objects. Because many of these 2Dscenes share the same properties (e.g., the shape or location of theintersection regions), the solution of one 2D slice may be used todetermine the solution of the next 2D slice; this may improve thecomputational efficiency.

The light sources may be positioned to lie in a plane. In oneembodiment, a number of “bar” light sources are combined with “point”light sources to accomplish more complex lighting arrangements. Inanother embodiment, multiple light arrays lying in a plane are combinedwith multiple outlier-resistant least squares fits to effectively reducethe computational complexity by incorporating previously known geometricparameters of the target object.

Referring to FIG. 24, in some embodiments, a shadow 2412 is cast on atranslucent or imaginary surface 2440 such that the shadow 2412 can beviewed and captured by a camera 2438. The camera 2438 may take pictureswith a number of light sensors (not shown in FIG. 24) arranged in arectangular grid. In the camera 2438, there may be three such gridsinterlaced at small distances that essentially lie directly on top ofeach other. Each grid has a different color filter on all of its lightsensors (e.g., red, green, or blue). Together, these sensors outputthree images, each comprising A×B light brightness values in the form ofa matrix of pixels. The three color images together form an A×B×3 RGBimage matrix. The image matrices may have their own coordinate system,which is defined by the set of matrix cell subscripts for a given pixel.For example, indices (x, y, z)=(0,0,0) may be defined and start in anupper left corner 2439 of the image. In one embodiment, the matrix ofz=1 represents the red color image and z=2 and z=3 are the green andblue images, respectively. In one implementation, an “image row” isdefined as all pixel values for a given constant coordinate value of yand an “image column” is defined as all pixel values for a givenconstant coordinate value of x.

Referring to FIG. 25A, a color image 2550 is split into images 2552,2554, 2556 of three primary colors (i.e., red, green, and blue,respectively) by decomposing an A×B×3 full color matrix in a memory into3 different A×B matrices, one for each z value between 1 and 3. Pixelsin each image 2552, 2554, 2556 are then compared to a brightnessthreshold value to determine which pixels represent shadow and whichrepresent background to thereby generate three shadow images 2558, 2560,2562, respectively. The brightness threshold value may be determined bya number of statistical techniques. For example, in some embodiments, amean pixel brightness is determined for each image and the threshold isset by subtracting three times the standard deviation of the brightnessof the same pixels in the same image. Edges of the shadow images 2558,2560, 2562 may then be determined to generate shadow point images 2564,2566, 2568, respectively, using a conventional edge-determiningtechnique. For example, the edge of each shadow image may be determinedby subtracting the shadow image itself from an offset image created byoffsetting a single pixel on the left (or right, top and/or bottom) sidethereof. The 2D approaches described above may be applied to each of theshadow point images 2564, 2566, 2568 to determine the locations andcolors of the objects. In some embodiments, shadow points in images2564, 2566, 2568 are combined into a single A×B×3 color matrix or image2570. Application of the 2D approaches described above to the combinedshadow point image 2570 can then reconstruct an image of the object 2572(e.g., a hand, as shown in FIG. 25B). Reconstructing an object (e.g., ahand) from shadows using various embodiments in the present inventionmay then be as simple as reconstructing a number of 2D ellipses. Forexample, fingers may be approximated by circles in 2D slices, and a palmmay be approximated as an ellipse. This reconstruction is therebyconverted into a practical number of simpler, more efficientreconstructions; the reconstructed 2D slices are then reassembled intothe final 3D solution. These efficient reconstructions may be computedusing a single processor or multiple processors operating in parallel toreduce the processing time.

In various embodiments, referring again to FIG. 24, the image coordinatesystem (i.e., the “imaging grid” 2442) is imposed on the surface 2440 toform a standard Cartesian coordinate system thereon such that the shadow2412 can be easily defined. For example, each pixel (or lightmeasurement value) in an image may be defined based on the coordinateintegers x and y. In some embodiments, the camera 2438 is perpendicularto the surface 2440 on which shadows 2412 are cast and a point on asurface in the image grid is defined based on its coordinate inside animage taken by the camera 2438. In one embodiment, all light sources liealong a line or lines on a plane perpendicular to one of the axes toreduce the computational complexity. In various embodiments, the z axisof the coordinate system uses the same distance units and isperpendicular to the x and y axes of image grid 2442 to capture the 3Dimages of the shadows. For example, the light sources may be placedparallel to the x or y axis and perpendicular to the z-axis; a 3Dcaptured shadow structure in the image coordinate system may be splitinto multiple 2D image slices, where each slice is a plane defined by agiven row on the imaging grid and the line of light sources. The 2Dslices may or may not share similar shapes. For example, the 2Dintersection region of a 3D intersection region for a spherical objectis very similar, i.e., a circle; whereas the 2D intersection region of a3D intersection region for a cone shape varies across the positions ofthe 2D slices.

As described above, the shape of multiple objects may be discerned bydetermining a minimal solution of each 2D slice obtained from the 3Dshadow. Since two slices next to each other are typically very similar,multiple slices often have the same minimal solution. In variousembodiments, when two nearby slices have the same number of intersectionregions, different combinations of the intersection regions are bypassedbetween the slices and the combination that works for a previous sliceis reused on the next slice. If the old combination works for the newslice, this solution becomes a new minimal solution for the new sliceand any further combinatorial checks are not performed. The reuse of oldcombinations thus greatly reduces computational time and complexity forcomplicated scenes. Although various embodiments described above arerelated to determining the shapes and positions of objects in 3D spaceusing cross-sections obtained from the shadows cast by the objects, oneof ordinary skill in the art will understand that cross-sectionsobtained utilizing different approaches, e.g., reflections from theobjects, are within the scope of the current invention.

In still other embodiments, a single camera can be used to capture animage of both the object and one or more shadows cast by the object fromone or more light sources at known positions. Such a system isillustrated in FIGS. 26A and 26B. FIG. 26A illustrates a system 2600 forcapturing a single image of an object 2602 and its shadow 2604 on asurface 2606 according to an embodiment of the present invention. System2600 includes a camera 2608 and a light source 2612 at a known positionrelative to camera 2608. Camera 2608 is positioned such that object ofinterest 2602 and surface 2606 are both within its field of view. Lightsource 2612 is positioned so that an object 2602 in the field of view ofcamera 2608 will cast a shadow onto surface 2606. FIG. 26B illustratesan image 2620 captured by camera 2608. Image 2620 includes an image 2622of object 2602 and an image 2624 of shadow 2604. In some embodiments, inaddition to creating shadow 2604, light source 2612 brightly illuminatesobject 2602. Thus, image 2620 will include brighter-than-average pixels2622, which can be associated with illuminated object 2602, anddarker-than-average pixels 2624, which can be associated with shadow2604.

In some embodiments, part of the shadow edge may be occluded by theobject. Where 30 the object can be reconstructed with fewer than fourtangents (e.g., using circular cross-sections), such occlusion is not aproblem. In some embodiments, occlusion can be minimized or eliminatedby placing the light source so that the shadow is projected in adifferent direction and using a camera with a wide field of view tocapture both the object and the unoccluded shadow. For example, in FIG.26A, the light source could be placed at position 2612′.

In other embodiments, multiple light sources can be used to provideadditional visible edge points that can be used to define tangents. Forexample, FIG. 26C illustrates a system 2630 with a camera 2632 and twolight sources 2634, 2636, one on either side of camera 2632. Lightsource 2634 casts a shadow 2638, and light source 2636 casts a shadow2640. In an image captured by camera 2632, object 2602 may partiallyocclude each of shadows 2638 and 2640. However, edge 2642 of shadow 2638and edge 2644 of shadow 2640 can both be detected, as can the edges ofobject 2602. These points provide four tangents to the object, two fromthe vantage point of camera 2632 and one each from the vantage point oflight sources 2634 and 2636.

As yet another example, multiple images of an object from differentvantage points can be generated within an optical system, e.g., usingbeamsplitters and mirrors. FIG. 27 illustrates an image-capture setup2700 for a motion capture system according to another embodiment of thepresent invention. A fully reflective front-surface mirror 2702 isprovided as a “ground plane.” A beamsplitter 2704 (e.g., a 50/50 or70/30 beamsplitter) is placed in front of mirror 2702 at about a20-degree angle to the ground plane. A camera 2706 is oriented towardbeamsplitter 2704. Due to the multiple reflections from different lightpaths, the image captured by the camera can include ghost silhouettes ofthe object from multiple perspectives. This is illustrated usingrepresentative rays. Rays 2706 a, 2706 b indicate the field of view of afirst virtual camera 2708; rays 2710 a, 2710 b indicate a second virtualcamera 2712; and rays 2714 a, 2714 b indicate a third virtual camera2716. Each virtual camera 2708, 2712, 2716 defines a vantage point forthe purpose of projecting tangent lines to an object 2718.

Another embodiment uses a screen with pinholes arranged in front of asingle camera. FIG. 28 illustrates an image capture setup 2800 usingpinholes according to an embodiment of the present invention. A camerasensor 2802 is oriented toward an opaque screen 2804 in which are formedtwo pinholes 2806, 2808. An object of interest 2810 is located in thespace on the opposite side of screen 2804 from camera sensor 2802.Pinholes 2806, 2808 can act as lenses, providing two effective vantagepoints for images of object 2810. A single camera sensor 2802 cancapture images from both vantage points.

More generally, any number of images of the object and/or shadows castby the object can be used to provide image data for analysis usingtechniques described herein, as long as different images or shadows canbe ascribed to different (known) vantage points. Those skilled in theart will appreciate that any combination of cameras, beamsplitters,pinholes, and other optical devices can be used to capture images of anobject and/or shadows cast by the object due to a light source at aknown position.

Further, while the embodiments described above use light as the mediumto detect edges of an object, other media can be used. For example, manyobjects cast a “sonic” shadow, either blocking or altering sound wavesthat impinge upon them. Such sonic shadows can also be used to locateedges of an object. (The sound waves need not be audible to humans; forexample, ultrasound can be used.) The term “shadow” is herein usedbroadly to connote light or sonic shadows or other occlusion of adisturbance by an object, and the term “light” means electromagneticradiation of any suitable wavelength(s) or wavelength range.

As described above, the general equation of an ellipse includes fiveparameters; where only four tangents are available, the ellipse isunderdetermined, and the analysis proceeds by assuming a value for oneof the five parameters. Which parameter is assumed is a matter of designchoice, and the optimum choice may depend on the type of object beingmodeled. It has been found that in the case where the object is a humanhand, assuming a value for the semimajor axis is effective. For othertypes of objects, other parameters may be preferred.

Further, while some embodiments described herein use ellipses to modelthe cross-sections, other shapes can be substituted. For instance, likean ellipse, a rectangle can be characterized by five parameters, and thetechniques described above can be applied to generate rectangularcross-sections in some or all slices. More generally, any simple closedcurve can be fit to a set of tangents in a slice. (The term “simpleclosed curve” is used in its mathematical sense throughout thisdisclosure and refers generally to a closed curve that does notintersect itself with no limitations implied as to other properties ofthe shape, such as the number of straight edge sections and/or vertices,which can be zero or more as desired.) The number of free parameters canbe limited based on the number of available tangents. In anotherembodiment, a closed intersection region (a region fully bounded bytangent lines) can be used as the cross-section, without fitting a curveto the region. While this may be less accurate than ellipses or othercurves, e.g., it can be useful in situations where high accuracy is notdesired. For example, in the case of capturing motion of a hand, if themotion of the fingertips is of primary interest, cross-sectionscorresponding to the palm of the hand can be modeled as the intersectionregions while fingers are modeled by fitting ellipses to theintersection regions.

In some embodiments, cross-slice correlations can be used to model allor part of the object using 3D surfaces, such as ellipsoids or otherquadratic surfaces. For example, elliptical (or other) cross-sectionsfrom several adjacent slices can be used to define an ellipsoidal objectthat best fits the ellipses. Alternatively, ellipsoids or other surfacescan be determined directly from tangent lines in multiple slices fromthe same set of images. The general equation of an ellipsoid includesnine free parameters; using nine (or more) tangents from two or three(or more) slices, an ellipsoid can be fit to the tangents. Ellipsoidscan be useful, e.g., for refining a model of fingertip (or thumb)position; the ellipsoid can roughly correspond to the last segment atthe tip of a finger (or thumb). In other embodiments, each segment of afinger can be modeled as an ellipsoid. Other quadratic surfaces, such ashyperboloids or cylinders, can also be used to model an object or aportion thereof.

In some embodiments, an object can be reconstructed without tangentlines. For example, given a sufficiently sensitive time-of-flightcamera, it would be possible to directly detect the difference indistances between various points on the near surface of a finger (orother curved object). In this case, a number of points on the surface(not limited to edge points) can be determined directly from thetime-of-flight data, and an ellipse (or other shape) can be fit to thepoints within a particular image slice. Time-of-flight data can also becombined with tangent-line information to provide a more detailed modelof an object's shape.

Any type of object can be the subject of motion capture using thesetechniques, and various aspects of the implementation can be optimizedfor a particular object. For example, the type and positions of camerasand/or light sources can be optimized based on the size of the objectwhose motion is to be captured and/or the space in which motion is to becaptured. As described above, in some embodiments, an object type can bedetermined based on the 3D model, and the determined object type can beused to add type-based constraints in subsequent phases of the analysis.In other embodiments, the motion capture algorithm can be optimized fora particular type of object, and assumptions or constraints pertainingto that object type (e.g., constraints on the number and relativeposition of fingers and palm of a hand) can be built into the analysisalgorithm. This can improve the quality of the reconstruction forobjects of that type, although it may degrade performance if anunexpected object type is presented. Depending on implementation, thismay be an acceptable design choice. For example, in a system forcontrolling a computer or other device based on recognition of handgestures, there may not be value in accurately reconstructing the motionof any other type of object (e.g., if a cat walks through the field ofview, it may be sufficient to determine that the moving object is not ahand).

Analysis techniques in accordance with embodiments of the presentinvention can be implemented as algorithms in any suitable computerlanguage and executed on programmable processors. Alternatively, some orall of the algorithms can be implemented in fixed-function logiccircuits, and such circuits can be designed and fabricated usingconventional or other tools.

Computer programs incorporating various features of the presentinvention may be encoded on various computer readable storage media;suitable media include magnetic disk or tape, optical storage media suchas compact disk (CD) or DVD (digital versatile disk), flash memory, andany other non-transitory medium capable of holding data in acomputer-readable form. Computer readable storage media encoded with theprogram code may be packaged with a compatible device or providedseparately from other devices. In addition program code may be encodedand transmitted via wired optical, and/or wireless networks conformingto a variety of protocols, including the Internet, thereby allowingdistribution, e.g., via Internet download.

The motion capture methods and systems described herein can be used in avariety of applications. For example, the motion of a hand can becaptured and used to control a computer system or video game console orother equipment based on recognizing gestures made by the hand.Full-body motion can be captured and used for similar purposes. In suchembodiments, the analysis and reconstruction advantageously occurs inapproximately real-time (e.g., times comparable to human reactiontimes), so that the user experiences a natural interaction with theequipment. In other applications, motion capture can be used for digitalrendering that is not done in real time, e.g., for computer-animatedmovies or the like; in such cases, the analysis can take as long asdesired. In intermediate cases, detected object shapes and motions canbe mapped to a physical model whose complexity is suited to theapplication—i.e., which provides a desired processing speed givenavailable computational resources. For example, the model may representgeneric hands at a computationally tractable level of detail, or mayincorporate the user's own hands by initial image capture thereoffollowed by texture mapping onto a generic hand model. The physicalmodel is manipulated (“morphed”) according to the detected objectorientation and motion.

Thus, although the invention has been described with respect to specificembodiments, it will be appreciated that the invention is intended tocover all modifications and equivalents within the scope of thefollowing claims.

In various embodiments, the system and method for capturing 3D motion ofan object as described herein may be integrated with other applications,such as a head-mounted device or a mobile device. Referring to FIG. 29A,a head-mounted device 2902 typically includes an optical assembly thatdisplays a surrounding environment or a virtual environment to the user;incorporation of the motion-capture system 2904 in the head-mounteddevice 2902 allows the user to interactively control the displayedenvironment. For example, the virtual environment may include virtualobjects that can be manipulated by the user's hand gestures, which aretracked by the motion-capture system 2904. In one embodiment, themotion-capture system 2904 integrated with the head-mounted device 2902detects a position and shape of user's hand and projects it on thedisplay of the head-mounted device 2902 such that the user can see hergestures and interactively control the objects in the virtualenvironment. This may be applied in, for example, gaming or internetbrowsing.

Referring to FIG. 29B, in some embodiments, the motion-capture system2904 is employed in a mobile device 2906 that communicates with otherdevices 2910. For example, a television (TV) 2910 may include an inputthat connects to a receiver (e.g., a wireless receiver, a cable networkor an antenna) to enable communication with the mobile device 2906. Themobile device 2906 first uses the embedded motion-capture system 2904 todetect movement of the user's hands, and to remotely control the TV 2910based on the detected hand movement. For example, the user may perform asliding hand gesture, in response to which the mobile device 2906transmits a signal to the TV 2910; the signal may be a raw trajectorythat circuitry associated with the TV interprets, or the mobile device2906 may include programming that interprets the gesture and sends asignal (e.g., a code corresponding to “sliding hand”) to the TV 2910.Either way, the TV 2910 responds by activating and displaying a controlpanel on the TV screen, and the user makes selections thereon usingfurther gestures. The user may, for example, move his hand in an “up” or“down” direction, which the motion-capture system 2904 embedded in themobile device 2906 converts to a signal that is transmitted to the TV2910, and in response, the user's selection of a channel of interestfrom the control panel is accepted. Additionally, the TV 2910 mayconnect to a source of video games (e.g., video game console orweb-based video game). The mobile device 2906 may capture the user'shand motion and transmit it to the TV for display thereon such that theuser can remotely interact with the virtual objects in the video game.

Referring to FIG. 29C, in various embodiments, the motion-capture system2904 is integrated with a security system 2912. The security system 2912may utilize the detected hand shape as well as hand jitter (detected asmotion) in order to authenticate the user 2914. For example, anauthentication server 2916 may maintain a database of users andcorresponding hand shapes and jitter patterns. When a user 2914 seeksaccess to a secure resource 2912, the motion-capture system 2904integrated with the resource 2912 (e.g., a computer) detects the user'shand shape and jitter pattern and then identifies the user 2914 bytransmitting this data to the authentication server 2916, which comparesthe detected data with the database record corresponding to theaccess-seeking user 2914. If the user 2914 is authorized to access thesecure resource 2912, the server 2916 transmits an acknowledgment to theresource 2912, which thereupon grants access. It should be stressed thatthe user 2914 may be authenticated to the secure system 2912 based onthe shape of any part of a human body that may be detected andrecognized using the motion-capture system 2904.

The terms and expressions employed herein are used as terms andexpressions of description and not of limitation, and there is nointention, in the use of such terms and expressions, of excluding anyequivalents of the features shown and described or portions thereof. Inaddition, having described certain embodiments of the invention, it willbe apparent to those of ordinary skill in the art that other embodimentsincorporating the concepts disclosed herein may be used withoutdeparting from the spirit and scope of the invention. Accordingly, thedescribed embodiments are to be considered in all respects as onlyillustrative and not restrictive.

What is claimed is:
 1. A smart phone having an interface that identifiesa position and a shape of a portion of a human hand moving in athree-dimensional (3D) space, the smart phone comprising: a camerahaving a particular vantage point configured to view the human hand; anda fixed function logic circuit storing instructions that, when executed,implement actions including: capturing, with the camera from theparticular vantage point, two or more images of a portion of a humanhand moving in the 3D space; analyzing the two or more images capturedby the camera from the particular vantage point to computationallyrepresent the portion of the human hand, as captured, as one or moremathematically represented 3D surfaces, each 3D surface corresponding toa cross-section of the portion of the human hand, based at least in parton a plurality of edge points of the portion of the human hand in theimage, tangent lines extending from the camera to at least two edgepoints of the plurality of edge points, and a centerline correspondingto the tangent lines; and reconstructing the position of, and the shapefitting, at least the portion of the human hand in the 3D space based atleast in part on the plurality of edge points and the centerline.
 2. Thesmart phone of claim 1, further including: at least one source thatcasts an output onto the portion of the human hand.
 3. The smart phoneof claim 1, further including transmitting to at least one furtherprocess, a signal that includes at least one selected from (i)trajectory information determined from the reconstructed position of,and the shape fitting, the at least a portion of the human hand that theat least one further process interprets, and (ii) gesture informationinterpreted from trajectory information for the portion of the humanhand by the smart phone.
 4. The smart phone of claim 1, furthercomprising a time-of-flight camera, and wherein a plurality of points onat least one surface of the portion of the human hand are determinedfrom time-of-flight data.
 5. The smart phone of claim 4, wherein thefixed function logic circuit further implements actions that combinetime-of-flight data with tangent-line information to provide a moredetailed model of the shape of at least the portion of the human hand.6. The smart phone of claim 1, wherein the fixed function logic circuitfurther implements actions that analyze the one or more surfaces toproduce a 3D model.
 7. The smart phone of claim 1, wherein the fixedfunction logic circuit further implements actions that refine a 3D modelby correlating a cross-section of a human hand portion represented by afirst surface with a cross-section of at least one different human handportion represented by at least one different 3D surface.
 8. The smartphone of claim 1, wherein the fixed function logic circuit furtherimplements actions that refines a 3D model based on at least one of ahuman hand type of a human hand comprising the portion of the human handand characteristics of the human hand type.
 9. The smart phone of claim1, wherein the fixed function logic circuit further implements actionsthat refines a 3D model by informing results of the analyzing withresults of such analyzing as conducted on images obtained at a differenttime and correspondingly modifying the 3D model.
 10. The smart phone ofclaim 1, wherein the fixed function logic circuit further implementsactions that refine a position of the portion of the human hand basedupon informing results of the analyzing with results of such analyzingas conducted on images obtained at a different time.
 11. The smart phoneof claim 1, wherein the fixed function logic circuit further implementsactions that determine constraints on at least one of a number andposition of one or more human hand portions according a human hand type.12. The smart phone of claim 1, wherein the fixed function logic circuitfurther implements actions that resolve an at least partially occludedportion of the human hand by conducting spatial correlations acrosssurfaces.
 13. The smart phone of claim 1, wherein the fixed functionlogic circuit further implements actions that capture one or moreadditional image sets of two or more images, and resolve an at leastpartially occluded portion of the human hand by conducting temporalcorrelations across image sets.
 14. The smart phone of claim 1, whereinthe fixed function logic circuit further implements actions that resolvean at least partially occluded portion of the human hand by applyingphysical constraints of a human hand type.
 15. The smart phone of claim1, wherein the fixed function logic circuit further implements actionsthat refine a 3D model formed by the reconstructing.
 16. The smart phoneof claim 15, wherein the 3D model represents a generic hand and therefining of the 3D model comprises texture mapping details from imagecapture onto a generic hand model.
 17. The smart phone of claim 15,wherein the fixed function logic circuit further implements actions thatmorph the 3D model according to detected human hand orientation andmotion.
 18. The smart phone of claim 15, wherein the refining of the 3Dmodel includes refining the 3D model based at least in part upon one ofcontinuity in motion and continuity in deformation.
 19. The smart phoneof claim 1, wherein the fixed function logic circuit further implementsactions that (i) refine a 3D model formed by the reconstructing bycomparing a reconstructed model of the portion of the human hand tohuman hand types in a library of human hand types and characteristicparameters for human hands in one or more possible poses, and (ii)assign matching human hand types to the 3D model when a match based oncharacteristic parameters is found.
 20. The smart phone of claim 19,wherein a human hand type includes a hand, a pose includes fingersextended and palm facing the camera, and the characteristic parametersinclude five fingers.
 21. The smart phone of claim 19, wherein therefining of the 3D model further comprises applying a constraint to the3D model based on characteristics of a human hand type.
 22. The smartphone of claim 21, wherein a human hand type includes a hand, and theconstraint includes positions and angles of fingers relative to eachother and to a palm portion of a hand.
 23. A method of using a smartphone to identify a position and a shape of a human hand moving in athree-dimensional (3D) space, the method comprising: configuring acamera of the smart phone to have a particular vantage point to view thehuman hand; and executing instructions on a fixed function logic circuitof the smart phone to implement actions including: capturing, with thecamera from the particular vantage point, two or more images of aportion of a human hand moving in the 3D space; analyzing the two ormore images captured by the camera from the particular vantage point tocomputationally represent the portion of the human hand, as captured, asone or more mathematically represented 3D surfaces, each 3D surfacecorresponding to a cross-section of the portion of the human hand, basedat least in part on a plurality of edge points of the portion of thehuman hand in the image, tangent lines extending from the camera to atleast two edge points of the plurality of edge points, and a centerlinecorresponding to the tangent lines; and reconstructing the position of,and the shape fitting, at least the portion of the human hand in the 3Dspace based at least in part on the plurality of edge points and thecenterline.
 24. A head mounted device, comprising: an optical assemblyto display a displayed environment including at least one of asurrounding three-dimensional (3D) environment and a virtualenvironment, the surrounding 3D environment including at least a portionof a human hand; and a smart phone having an interface that identifies aposition and a shape of a portion of the human hand moving in thesurrounding 3D environment, the smart phone including: a camera having aparticular vantage point configured to view the human hand; and a fixedfunction logic circuit storing instructions that, when executed,implement actions including: capturing, with the camera from theparticular vantage point, two or more images of a portion of a humanhand moving in the surrounding 3D environment; analyzing the two or moreimages captured by the camera from the particular vantage point tocomputationally represent the portion of the human hand, as captured, asone or more mathematically represented 3D surfaces, each 3D surfacecorresponding to a cross-section of the portion of the human hand, basedat least in part on a plurality of edge points of the portion of thehuman hand in the image, tangent lines extending from the camera to atleast two edge points of the plurality of edge points, and a centerlinecorresponding to the tangent lines; and reconstructing the position of,and the shape fitting, at least the portion of the human hand in thesurrounding 3D environment based at least in part on the plurality ofedge points and the centerline.